Conference on Quantum Matter in Low Dimensions: Opportunities and Challenges
Albanova University Center, room FD5
We note that participation is limited, and therefor recommend early registration. The dead-line has been extended to August 1st.
The speakers for the conference are:
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This conference is part of a four week workshop held at Nordita. Information on this workshop, can be found on the workhop website.
This conference is supported by INSTANS, the Swedish research council and Nordita.
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Registration
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Opening of the conferenceSpeaker: Lárus Thorlacius and scientific coordinators
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Five years of INSTANSSpeaker: Giuseppe Mussardo (SISSA, Chair of INSTANS steering committee)
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Graphene: relativistic electrons in carbon flatlandThe recent discovery of graphene, a one-atom thick membrane of crystalline Carbon, has opened an extraordinary arena for new physics and applications stemming from charge carriers that are governed by quantum-relativistic dynamics. I will review the physical properties of this material and present recent experimental results obtained with scanning tunneling microscopy and magneto-transport which provided access to the unusual charge carriers in graphene. The findings include direct observation of the Landau level energy spectrum that governs the motion of the relativistic charge carriers in a magnetic field, observation of the fractional quantum Hall effect and a magnetically induced insulating phase. Scanning tunneling microscopy image of graphene showing the honeycomb arrangement of Carbon atoms.
G. Li, A. Luican and E. Y. Andrei, Phys. Rev. Lett 102, (2009).Speaker: Eva Andrei (Rutgers University) -
Coffee and Registration
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Strains and gauge fields in grapheneLattice deformations couple to electrons in graphene by giving rise to an effective gauge field[1,2]. This unique feature leads to the possibility of modifying the electronic properties by applying strain to the lattice[3,4]. The main properties of the interaction between electrons and long wavelength lattice deformations will be reviewed.
[1] A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, Rev. Mod. Phys. 81, 109 (2009)
[2] M. A. H. Vozmediano, M. I. Katsnelson, F. Guinea, Phys. Rep., in press (2010).
[3] F. Guinea, M. I. Katsnelson, A. K. Geim, Nature Phys. 6, 30 (2010).
[4] N. Levy, S. A. Burke, K. L. Meaker, M. Panlasigui, A. Zettl, F. Guinea, A. H. Castro Neto, and M. F. Crommie, Science 329, 544 (2010).Speaker: Francisco Guinea (CSIC, Madrid) - 5
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Lunch
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Cold atoms in 1D in and out of equilibriumTBASpeaker: David Weiss (Pennsylvania State University)
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Quantum critical behavior in driven and strongly interacting Rydberg gasesWe study the appearance of correlated many-body phenomena in an ensemble of atoms driven resonantly into a strongly interacting Rydberg state. The ground state of the Hamiltonian describing the driven system exhibits a second order quantum phase transition. We derive the critical theory for the quantum phase transition and show that it describes the properties of the driven Rydberg system in the saturated regime. We find that the suppression of Rydberg excitations known as blockade phenomena exhibits an algebraic scaling law with a universal exponent. Special focus is on the system in one dimension in the presence of an underlying lattice structure, where we will show that in the driven system a two-stage melting takes place from a commensurate solid into a floating solid phase and finally into a paramagnetic phase.Speaker: Hans Peter Büchler (Universität Stuttgart)
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Coffee break
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Competing orders in one-dimensional multicomponent cold fermionsWe investigate the nature of the Mott-insulating phases of half-filled 2N-component cold fermions loaded into a 1D optical lattice by means of a low-energy approach and large-scale DMRG calculations. For attractive interactions, we find the emergence of gapless and gapped phases depending on the parity of N. The analogue of the Haldane phase of the Heisenberg chain with integer spin is stabilized for integer N with hidden-ordering and edge states.Speaker: Philippe Lecheminant (LPTM, Université de Cergy-Pontoise)
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Poster Session I (with snacks and beverages)
Poster presenters:
BALLMANN, Katinka:
Mr. BAUER, Florian:
Mr. BEUGELING, Wouter:
Chern-Simons theory of multi-component quantum Hall
systems
The fractional quantum Hall effect is conveniently described
by a
Chern-Simons based composite-fermion approach. The
Hamiltonian theory of
Shankar and Murthy [Rev. Mod. Phys. 75, 1101 (2003)]
proves to be a
useful model to compute physical quantities.
On this poster we present an extension of this model to
systems for
which internal degrees of freedom (spin and pseudospin) are
relevant,
such as bilayer systems and graphene.
Mr. BRANDINO, Giuseppe Piero:
Energy level distribution of perturbed
conformal field theories
We study the energy level spacing of perturbed conformal
minimal
models in finite volume, considering perturbations of such
models that are
massive but not necessarily integrable. We compute their
spectrum using a
renormalization group improved truncated conformal
spectrum approach. With
this method we are able to study systems where more than
40 000 states are kept
and where we determine the energies of the lowest several
thousand eigenstates
with high accuracy. We find, as expected, that the level
spacing statistics of
integrable perturbed minimal models are Poissonian while
the statistics of nonintegrable
perturbations are GOE-like. However, by varying the system
size (and so controlling the
positioning of the theory between its IR and UV limits) one
can induce crossovers between
the two statistical distributions.
Mr. CAGNANI, Ivan:
Ms. CANOVI, Elena:
We discuss how thermalization following a quantum quench
in a strongly
correlated quantum system is intimately connected to
many-body
localization in the space of quasi-particles. We test our
picture in the
anisotropic Heisenberg spin chain with an integrability-
breaking term. We
first quantify the deviations from integrability by analyzing
the level
spacing statistics and the charac- teristics of the system
eigenstates. We
then focus on thermalization by studying the dynamics
after a sudden
quench of the anisotropy parameter.
arXiv:1006.1634
Dr. CHUDZINSKI, Piotr:
Spin rotational symmetry breaking by orbital current
patterns in
two-leg ladders
P. Chudzinski, M. Gabay, and T. Giamarchi
We investigate the physical consequences of orbital current
patterns
(OCP) in doped two-leg Cu-O Hubbard ladders. The internal
symmetry of
the pattern, in the case of the ladder structure, differs
slightly
from that suggested so far for cuprates. We focus on this
OCP and look
for measurable signatures of its existence. We compute the
magnetic
field produced by the OCP at each lattice site and estimate
its value
in view of a possible experimental detection. Using a
renormalization-group (RG) analysis, we determine the
changes that are
caused by the SU(2) spin rotational symmetry breaking
which occurs
when the OCP is present in the ground-state phase
diagram. The most
significant one is an in-plane spin-density wave gap opening
in an
otherwise critical phase, at intermediate dopings. We
estimate the
value of this gap, give an analytic expression for the
correlation
functions and examine some of the magnetic properties of
this new
phase which can be revealed in measurements. We
compute the
conductance in the presence of a single impurity using an
RG analysis.
A discussion of the various sources of SU(2) symmetry
breaking
underscores the specificity of the OCP-induced effects.
Mr. DALMONTE, Marcello:
Atomic color superfluidity via three-body loss
Large three-body loss rates in a three-component Fermi gas
confined in an optical lattice can dynamically
prevent atoms from
tunneling so as to occupy a lattice site with three atoms.
This effective constraint not only suppresses the
occurrence of
actual loss events, but stabilizes color-like BCS-pairing
phases by suppressing the formation of trions. We
study the effect of
the constraint on the many-body physics using bosonization
and density matrix renormalization group
techniques, and also
investigate the full dissipative dynamics including loss for
the example of $^6$Li.
A. Kantian, M. Dalmonte, S. Diehl, W. Hofstetter, P. Zoller
and A. J. Daley, Phys. Rev. Lett. {\bf 104}, 240401
(2009)
Mr. DE LUCA, Andrea:
Prof. EGGERT, Sebastian:
Dr. ERMANN, Leonardo:
Dr. ESTIENNE, Benoit:
Electron-quasihole duality in Read-Rezayi states and Jack
wavefunctions
We consider the quasihole wavefunctions of the non-abelian
Read-Rezayi quantum Hall states which are given by the
conformal
blocks of the minimal model WA_{k-1}(k+1,k+2) of the
WA_{k-1} algebra. By studying the degenerate
representations of this
conformal field theories, we derive a second order
differential equation satisfied by a general many-quasihole
wavefunction. We
find a duality between the differential equations fixing the
electron and quasihole wavefunctions. They both satisfy the
Laplace-
Beltrami equation. We use this equation to obtain an
analytic expression for the generic wavefunction with one
excess flux.
These results also apply to the more general models
WA_{k-1}(k+1,k+r) corresponding to the recently
introduced Jack states
Mr. FAGOTTI, Maurizio:
Mr. FERRARO, Dario:
Multiple-quasiparticles tunnelling between fractional
quantum Hall edge states
A detailed description of tunnelling processes through a
point contact for fractional quantum Hall edges in the Jain
series will be
presented. Edge states will be
described in terms of charged and neutral modes
propagating with finite velocities. Possible interaction effects
due to external
environment will be properly
taken into account.
We will show that multiple-quasiparticle agglomerates
dominate on single quasiparticle in the low energy regime.
This result
crucially depends on the presence
of finite bandwidth neutral modes and is essential to explain
the observed anomalous behaviour of tunnelling
conductance and
noise through a point contact
[1, 2]. The temperature behaviour of linear conductance
and effective charge estimated from the current noise will
be presented
and compared with
experiments [3, 4, 5].
[1] Y.C. Chung, M. Heiblum, V. Umansky, Phys. Rev. Lett.
91, 216804 (2003).
[2] A. Bid, N. Ofek, M. Heiblum, V. Umansky, D. Mahalu,
Phys. Rev. Lett. 103, 236802 (2009).
[3] D. Ferraro, A. Braggio, M. Merlo, N. Magnoli, M. Sassetti,
Phys. Rev. Lett. 101, 166805 (2008).
[4] D. Ferraro, A. Braggio, N. Magnoli, M. Sassetti, New J.
Phys. 12, 013012 (2010).
Mr. FIORETTO, Davide:
Quantum quenches in integrable field theories
We study the non equilibrium time evolution of an
integrable
field theory in 1+1 dimensions after a sudden variation of a
global
parameter of the Hamiltonian. For a specific class of
quenches, we compute
the expectation value of any local operators for long times
as a series of
form factors. In this way, we are able to show that this
asymptotic value
can be obtained by a generalized Gibbs ensemble with a
different effective
temperature for each eigenmode.
Dr. FRANCHINI, Fabio:
Nonlinear dynamics of spin and charge in spin-Calogero
model
We study the full, nonlinear dynamics of spin and charge in
the
spin-Calogero model, by constructing a collective, i.e.
hydrodynamic,
description of the model.
The latter is an integrable 1-D model of quantum spin-1/2
particles
interacting through inverse-square interaction and
exchange.
We construct the collective Hamiltonian in a semi-classical
regime where
gradient corrections to the exact hydrodynamic formulation
of the theory
may be neglected.
In this approximation, the equations of motion can be
decoupled and
written as to a set of independent Riemann-Hopf (or inviscid
Burgers')
equations for the dressed Fermi momenta.
We study the dynamics of some non-equilibrium spin-
charge configurations
for times smaller than the time-scale of the gradient
catastrophe and we
find an interesting interplay between spin and charge
degrees of freedom.
We also consider the limit of large coupling parameter and
show that the
resulting hydrodynamics for the spin sector describes the
so-called
Haldane-Shastry model.
Finally, we show how this hydrodynamic description allows
for the
calculation of correlation functions that cannot be
considered with
conventional bosonization, such as the Emptiness
Formation Probability.
- M. Kulkarni, F. Franchini, A. G. Abanov; Physical Review B
80, 165105
(2009)
- F. Franchini, M. Kulkarni; Nucl.Phys.B825:320-340,2010
Dr. GARCIA GARCIA, antonio:
Mr. GHAZARYAN, Areg:Dr. SATO, Masahiro:
Spin dynamics in multipolar phases of one-dimensional
quantum frustrated ferromagnet
Recently, it has been shown that spin
nematic (quadrupolar) or higher multipolar correlation
functions exhibit
a quasi long- range order in the broad range of the field-
induced
Tomonaga-Luttinger-liquid (TLL) phase in spin-1/2
frustrated chains.
We show [1,2] that the temperature and field dependence
of the NMR relaxation rate
1/T1 in these multipolar TLLs is qualitatively different from
that
in conventional TLLs of one-dimensional quantum magnets
such
as the spin-1/2 Heisenberg chain; 1/T1 decreases with
lowering temperature
in high-field region of multipolar TLL, and it also decreases
with increasing
a magnetic field. These behaviors can be used as an indirect
but
definite signature for identifying the multipolar order. We
also discuss
some characteristic features of spin dynamical structure
factors.
[1] M.Sato, T.Momoi and A.Furusaki, PRB79, 060406(R)
(2009).
[2] M.Sato, T.Hikihara and T.Momoi, in preparation.
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Majorana-Shockley states in topological superconductorsVortices in two-dimensional superconductors with broken time-reversal and spin-rotation symmetry can bind states at zero excitation energy. These socalled Majorana bound states transform a thermal insulator into a thermal metal and may be used to encode topologically protected qubits. We identify an alternative mechanism for the formation of Majorana bound states, akin to the way in which Shockley states are formed on metal surfaces: An atomic-scale electrostatic line defect can have a pair of Majorana bound states at the end points. The Shockley mechanism explains the appearance of a thermal metal in vortex-free lattice models of chiral p-wave superconductors and (unlike the vortex mechanism) is also operative in the topologically trivial phase.Speaker: Carlo Beenakker (Leiden University)
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Quantum Imaging of Topologically Ordered MatterDeforming a material and restoring it precisely back to its starting point intuitively implies that the material before and afterwards is identical. This is true classically, and was believed to be true in general until recently in the history of quantum mechanics. Even if all the atoms, electrons, and other ingredients are returned exactly to where they started, we now know that the restored material can differ from the undeformed material by nontrivial quantum mechanical phase factors. These Berry phases have garnered increasing appreciation in recent years, and in condensed matter they arise from the topology of electronic states and embedded degeneracies. Such considerations have helped to identify new ground states consisting of topologically ordered matter, which can be exploited in quantum devices, quantum computing strategies, and in searches for exotic particles. This talk will overview new experiments from our lab, employing scanning tunneling microscopy and atomic manipulation, that directly visualize and control topological order in several materials and nanostructures.Speaker: Hari Manoharan (Stanford University)
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Coffee break
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Quantum magnetism and interaction effects in topological insulatorsWe discuss connections between models of magnetism exhibiting topological order and topological band insulators. In this context, we also explore interaction effects in topological insulators with particular emphasis on lattice models with Dirac and quadratic band crossing points in the non-interacting limit. Our work reveals connections between seemingly unrelated topological systems.Speaker: Gregory Fiete (University of Texas, Austin)
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Fermion transfer by vortex tunnelingWe study a Fabry-Perot interferometer made out of magnetic and superconducting regions on the surface state of a 3D topological insulator. In particular we investigate the possibility of transferring a chiral edge Majorana fermion between two counter-propagating edges by the tunneling of two superconducting vortices across the superconducting region. This process is potentially useful for topological charge measurement.Speaker: Johan Nilsson (University of Gothenburg)
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Lunch
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Dynamics of one-dimensional correlated systems with and without disorderCorrelated systems with relatively low entanglement entropy can be studied efficiently by DMRG-type methods. An analytical theory for how the central charge controls "finite-entanglement scaling" for static properties is briefly reviewed; we then turn to dynamics. Two situations considered, for which numerical results are possible on large systems even without integrability, are a sweep through a quantum critical point and the possible existence of glassy behavior in infinite-temperature dynamics of 1D systems ("many-body localization").Speaker: Joel Moore (University of California, Berkeley)
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Entanglement entropy of disconnected regions in extended systemsThe study of the entanglement poperties of the ground-state of an extended quantum systems has prompted an intense research activity at the crossroad of different disciplines such as statistical mechanics, quantum information, and quantum filed theory. Quantifying the entanglement allowed an elegant and finer characterization of many extended quantum systems. In this talk I present the recent results on entanglement of disconnected regions for one-dimensional systems at a quantum critical point that are described by a conformal invariant field theory.Speaker: Pasquale Calabrese (Universita' di Pisa)
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Coffee break
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Hierarchy of edge-locking effects in interacting 1D lattice systemsIn one-dimensional lattices with open boundaries, I will present a `fractal' structure high up in the energy specturm, and associated out-of-equilibrium consequences.
The non-equilibrium consequences are a hierarchy of `edge-locking' effects.
I will show versions of the phenomenon for three classic condensed-matter models:
(1) the Bose-Hubbard model;
(2) the spinless fermion model with nearest-neighbor repulsion;
(3) the XXZ (Heiseberg-Ising) spin chain.Speaker: Masudul Haque (MPI-PKS Dresden) -
Poster Session II (with snacks and beverages)
Poster presenters:
Mr. ALBA, vincenzo:
Entanglement entropy of two disjoint blocks in critical Ising
models
I will present results about the scaling of the Renyi and
entanglement entropy of two disjoint blocks of critical Ising
models, as function of their sizes and separations. I will
present analytic results based on conformal field theory that
are quantitatively checked in numerical simulations of both
the quantum spin chain and the classical two dimensional
Ising model. Theoretical results match the ones obtained
from numerical simulations only after taking properly into
account the corrections induced by the finite length of the
blocks.
Mr. HAMZELOUI, Saeed:
Dr. HOU, Chang-Yu:
KAILASVUORI, Janik:
Finite Conductivity Minimum in Bilayer Graphene without
Charge Inhomogeneities
Boltzmann transport theory fails near the linear band-
crossing of single-layer graphene and near the quadratic
band-crossing of bilayer
graphene. We report on a numerical study which assesses
the role of inter-band coherence in transport when the
Fermi level lies near the
band-crossing energy of bilayer graphene. We find that
interband coherence enhances conduction, and that it plays
an essential role in
graphene's minimum conductivity phenomena. This
behavior is qualitatively captured by an approximate theory
which treats inter-band
coherence in a relaxation-time approximation. On the basis
of this short-range-disorder model study, we conclude that
electron-hole puddle
formation is not a necessary condition for finite conductivity
in graphene at zero average carrier density.
Mr. LAHTINEN, Ville:
Interacting anyons and gauge field driven topological phase
transitions
The exact solvability of the honeycomb lattice model offers
an ideal
platform to study phase transitions between different
topological
phases. Here we show the existence of a previously
undiscovered
topological phase that supports chiral Abelian anyons. It
appears due
to a presence of a vortex lattice that we can relate to a
staggering
of the model's couplings. By considering the effect of
coupling
distortions on the low-energy theory of Dirac fermions, we
show that
different phase transition driving perturbations translate to
different chiral gauge fields. These lead to distinct Fermi
surface
evolutions that characterize the phase transitions. Finally,
we
demonstrate how the transition can also be understood as
arising due
to interactions between the anyonic vortices.
Mr. LEVKIVSKYI, Ivan:
Noise-Induced Phase Transition in the Electronic Mach-
Zehnder
Interferometer
Recently, Aharonov-Bohm (AB) effect in electronic
Mach-Zehnder (MZ) interferometers has attracted much
attention among
experimental and theoretical physicists. These
interferometers, for
the first time experimentally realized in the group of
Heiblum [1],
utilize quantum Hall edge states in place of optical beams,
and
quantum point contacts (QPC) as beam splitters, to partition
edge
channels. Theoretical attempts to explain experimentally
observed
puzzling lobe-type behavior of the visibility of AB oscillations
as a
function of voltage bias [2-5], have led to a number of
publications
[6-9]. They have focused on the filling factor ν=1 state, and
suggested different mechanisms of dephasing, including the
resonant
interaction with a counter-propagating edge state [6], the
dispersion
of the Coulomb interaction potential [7], and non-Gaussian
noise
effects [8,9]. To date, however, all the experiments,
reporting
multiple side lobes in the visibility function of voltage bias,
have
been done at filling factor ν=2. We will argue that, in fact,
there
are two main mechanisms of dephasing in MZ
interferometers. One
mechanism [10], due to spontaneous emission of edge
magneto-plasmons,
leads to a size effect, which explains the lobes and many
other
details of experiments [2-5]. According to the second
mechanism [11],
dephasing in electronic MZ interferometers is due to an
external
non-equilibrium noise source. Experimentally [2], such a
noise is
created with the help of an additional QPC with the
transparency T
that partitions incident edge channels. We predict that a
phase
transition occurs at T=1/2, where the visibility function of
voltage
bias sharply changes its behavior. An important role in this
phenomenon is played by a non-Gaussianity of noise, which
is typically
negligible because of a weak coupling. It turns out that MZ
interferometers are strongly coupled to noise. They,
therefore, can be
considered efficient detectors of full counting statistics [12].
References:
[1] Y. Ji et al., Nature (London) 422, 415 (2003).
[2] I. Neder et al., Phys. Rev. Lett. 96, 016804
(2006).
[3] E. Bieri et al., Phys. Rev. B 79, 245324 (2009).
[4] P. Roulleau et al., Phys. Rev. B 76, 161309(R)
(2007).
[5] L.V. Litvin et al., Phys. Rev. B 75, 033315 (2007).
[6] E.V. Sukhorukov, and V.V. Cheianov, Phys. Rev. Lett.
99, 156801 (2007).
[7] J.T. Chalker, Y. Gefen, and M.Y. Veillette, Phys. Rev. B
76, 085320 (2007).
[8] S.-C. Youn, H.-W. Lee, and H.-S. Sim, Phys. Rev. Lett.
100, 196807 (2008).
[9] I. Neder and E. Ginossar, Phys. Rev. Lett. 100, 196806
(2008).
[10] I.P. Levkivskyi, and E.V. Sukhorukov, Phys. Rev. B 78,
045322 (2008).
[11] I.P. Levkivskyi, E.V. Sukhorukov, Phys. Rev. Lett. 103,
036801 (2009).
[12] L.S. Levitov, H. Lee, and G.B. Lesovik, J. Math. Phys.
37, 4845 (1996).
Mr. MACRI, Tommaso:
Dynamics of Cold-Atom Fermi Mixtures
Mrs. MIILBAEVA, Guljamal:
MOZGUNOV, E:
Excitation spectrum of a 2D long-range Bose liquid with a
supersymmetry
Specic model of a 2D Bose liquid with non-relativistic
supersymmetry [1, 2] is studied numerically
by means of a mapping to a classical Langevin dynamics [3,
4]. The model contains dimensionless
coupling constant . At small 1 this model is very similar to
the 2D Bose-lqiuid with pair-wise
logarithmic interaction and thus exibit superuid ground
state. At very large 35 the ground
state nearly breaks translational symmetry: equal-time
density correlations in the emergent ground
state are equivalent to those of the classical 2D crystal at
nonzero temperature. We have studied the
excitation spectrum of this model in the whole range of by
means of the analysis of the dynamic
structure factor S(k, t) computed for the equivalent classical
model, like it was done in Ref. [5] for the
model of quantum dimers at the Rokshar-Kivelson point [6].
The spectrum !(q) we found contains
a plasmon gap !0 at q = 0 and a well-dened roton minimum
at q = q0 = 2
p
n with minimal
excitation energy . The ratio /!0 decreases sharply with in
the whole range of the strongly
coupled Bose liquid 1 < < 35, down to very small values
10−2. However, we could not detect,
with our numerical accurace, a vanishing of the roton gap
before 2D crystallization transition takes
place at = c 37.We thus conclude that the ground-state is
of superuid nature (at T = 0) in the
whole range of < c (however, the critical temperature Tc of
superuid transition drops sharply
with ). In the crystalline state > c no well-dened low-
energy excitations corresponding to
shear modes was found, in agreement with theoretically
expected spectrum !(k) / k2 that suggests
strongly decaying nature of the corresponding
quasiparticles.
[1] M. V. Feigel'man and M. A. Skvortsov. Nucl. Phys. B 506
[FS], 665 (1997), arXiv:cond-mat/9703215v1
[2] C. Kane, S. Kivelson, Lee and Zhang Phys. Rev. b
(1991)
[3] M. V. Feigel'man and A. M. Tsvelik, Sov.Phys. JETP
(1982)
[4] C.L. Henley, J. Phys.: Condens. Matter 16, S891
(2004).
[5] A. M. Lauchli, S. Capponi and F. F. Assaad, J. Stat. Mech.
(2008) P01010
[6] D. Rokhsar and S. Kivelson, Phys. Rev. Lett. 61, 2376
(1988).
Dr. OHANYAN, Vadim:
Spontaneous translational symmetry breaking associate magnetization
plateaus in one-dimensional spin systems with Ising and Heisenberg
bonds
There are well known examples of integrable many-particle systems solvable
within the Bethe ansatz technique,
like 1d Heisenberg chain, Hubbard model, e.t.c. Though, Bethe ansatz, being a
paradigm in modern theoretical and
mathematical physics, is very important by itself, its application in condensed
matter physic is still very restricted.
Particularly, in the physics of magnetism one usually needs to describe
thermodynamic properties of certain quantum
spin-lattice models at ¯nite temperature. At the moment exact treatment of this
problem is feasible only for very
limited number of model within rather complicated and sophisticated techniques
like quantum transfer matrix
and non-liner integral equation. However, majority of real magnetic materials
(even one-dimensional) has lattice
structure which corresponds to no known integrable models. Thus, numerical
calculations are almost the only way
to shed a light into their thermodynamic properties. However, one can change a
little underlying spin system to get
the model, which can be easily solved exactly within classical transfer-matrix
technique. Namely, if one change some
interaction bonds with Ising ones in such a way that Hamiltonian of the
emergent system be a sum of commuting
operator, then one can expand the exponential in the partition function and get
the formal structure which is
suitable to applying the classical transfer matrix method. Thus, one will obtain a
one-dimensional spin system with
clusters of quantum spins and intermediate "classical" spins between them. The
problem of calculation the partition
function of the system yield the problem of diagonalization of the small quantum
spin clusters which in most cases
are feasible and further calculation of the eigenvalues of classical transfer matrix
which is also straightforward. A
various spin systems with Ising and Heisenberg bonds have been considered
recently, e.g. diamond-chain, alternating
linear chain, chains of triangle quantum cluster, sawtooth chain, orthogonal-
dimer chain, e.t.c. Here we would like
to emphasize one particular phenomena which is inherent to such a systems
where left and right side neighboring of
each cluster of quantum spins are non equivalent to each other. On the example
of two systems, the sawtooth chain
with quantum clusters of two spins and orthogonal-dimer chain with quantum
cluster of three spins in triangular
topology, we demonstrate the appearance of magnetization plateau at M=Msat =
1=4 which is connected with
breaking of translational symetry of the lattice, more precisely with the doubling
of unit cell. Solving the problem
of partition function calculation exactly we also obtain analytic expressions for
free energy and all thermodynamic
function, presenting the plots of magnetization processes for ¯nite temperature
displaying magnetization plateaus
at M=Msat = 0; 1=4; 1=2. Analyzing ground states properties we obtain T = 0
ground states phase diagrams with
exact description of all transition lines and triple points.
Prof. PROTOGENOV, Alexander:
A chain of strongly correlated $SU(2)_{4}$ anyons
L. Martina, A. Protogenov, V. Verbus
One-dimensional lattice model of $SU(2)_{4}$ anyons
containing a transition into
the topological ordered phase state is considered. An
effective low-energy Hamiltonian
is found for half-integer and integer indices of the type of
strongly correlated non-Abelian
anyons. The Hilbert state space properties of the considered
modular tensor category are studied.
Mr. QAIUMZADEH, Alireza:
Mr. RAHIMI, Mojtaba:
Prof. RAO, Sumathi:
Dr. RUTKEVICH, Sergei:
Kink confinement in the $1d$-quantum ferromagnet
$\mathrm{Co}\mathrm{Nb}_2\mathrm{O}_6$.
Calculation of bound-state energies and intensities.
Recently Coldea {\it et al} (2010 Science {\bf 327} 177)
reported observation
of the weak confinement of kinks in the Ising spin chain
ferromagnet
$\mathrm{Co}\mathrm{Nb}_2\mathrm{O}_6$
at low temperatures. To interpret the entire spectra of
magnetic excitations measured via neutron scattering,
they introduce a phenomenological model, which takes into
account only the two-kink configurations of the
spin chain.
We describe the exact solution of this model. The explicit
expressions for the two-kink bound-state energy
spectra
and for the relative intensities of neutron scattering on
these magnetic modes are derived in terms of the
Bessel function.
Dr. SALOMOV, Uktam:
Dr. SATO, Masahiro:
Ferromagnetic transition in one-dimensional spin-1/2 Bose
and Fermi gases
Internal degrees of freedom in many-body systems
generally
provide a variety of phenomena, as electron spins in solids
generate
various magnetic structures. As the simplest system with
internal degrees
of freedom we study one-dimensional two-component
(pseudospin-1/2)
Bose/Fermi gas, which could be realized by using ultra-cold
atoms. If
a strong repulsion is introduced between two components, a
spontaneous
population imbalance (i.e., ferromagnetism) is expected to
appear.
However, it is known that the existent weak- and strong-
coupling
theories cannot capture the nature of the imbalanced phase
and the ordering.
We have thoroughly studied them [1] by combining
numerical approaches
(exact diagonalization and infinite time-evolving block
decimation) with
some analytic methods in an efficient manner. It is shown
that (i)
the universality class of the ferromagnetic transition
drastically changes
from first order to an Ising type when an inter-component
hopping is
introduced, and (ii) the imbalanced phase has a gapless
charge mode
and a gapped spin one.
[1] S.Takayoshi, M.Sato and S.Furukawa, PRA81, 053606
(2010).
Dr. SEDLMAYR, Nicholas:
Non-Collinear Ferromagnetic Luttinger Liquids
The presence of the electron-electron interaction in one
dimension profoundly changes the properties of a system.
The separation of charge and spin degrees of freedom is just
one example. Though such an effect does not survive in the
ferromagnetic case, a diagonal basis can still be found for
the appropriate quasi-particles. This will have consequences
for spin-transfer-torque effects. We consider what happens
when a ferromagnetic one dimensional interacting system
(more specifically a Luttinger liquid) has a region of non-
collinearity present, \emph{i.e.}~a domain wall. The
presence of the domain wall introduces a spin dependent
scatterer into the problem, an idea which has already
received some attention in the limit of weak magnetization.
In this work we would like to go further and look at how
this affects the transport properties of the Luttinger liquid,
and also how the magnetization dynamics of the domain
wall are modified for a Luttinger liquid.
SOLUYANOV, Alexey:
Dr. TEZUKA, Masaki:
Effect of disorder on 1D ultracold Fermi atomic gases
Cold atom experiments have made it possible to realize
quantum degenerate matter with controlled disorder and
interactions
with unprecedented precision. This presents an ideal setting
for the
study of novel phases of quantum matter and quantum
phase transitions,
such as the FFLO phase in harmonically trapped 1D system
of
population-imbalanced Fermi gases [1]. Specifically,
introduction of a
multichromatic potential [2] to a system of 2D array of 1D
Fermi gases
[3] would allow the study of the effect of disorder on
fermionic
superfluidity. While true long-range pairing order is
forbidden in 1D,
superfluidity is possible in a finite-size system.
We have studied a 1D Fermi gas with attractive short-
ranged
interactions in a multichromatic potential by the density-
matrix
renormalization group (DMRG) method [4]. We have
identified a region
of parameters where the disorder enhances pairing. When
the disorder
is further increased, global superfluidity eventually breaks
down. The
separation between the disorder strengths at superfluidity
breakdown
and the insulating transition suggests that the intermediate
“pseudo-gap” phase is characterized by strong pairing
without quasi
long-range order.
[1] M. Tezuka and M. Ueda, New J. Phys. 12, 055029
(2010) and
references therein.
[2] G. Roati et al., Nature 453, 895 (2008).
[3] Y. A. Liao et al., arXiv:0912.0092v2 (preprint).
[4] M. Tezuka and A.M. García-García, arXiv:0912.2263
(preprint).
Dr. TOTH, Anna:
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Incompressibility, quantum geometry, and Hall viscosity in the FQHEMost recent work on FQHE states focusses on their topological properties, and take the existence of incompressibility for granted. I will describe how recent developments concerning the dissipationless "Hall viscosity" property surprisingly turn out to be related to incompressibility properties investigated many years ago by Girvin, Macdonald and Platzman, and provide new insights into the quantum geometry of incompressibility.Speaker: Duncan Haldane (Princeton University)
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Coffee break
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Novel Phases: From Photons to ElectronsRecently, theoretical studies have advertised electromagnetic resonator (photon) arrays in circuit QED, coherently coupled to artificial atoms (e.g., superconducting qubits) as a new venue for constructing quantum simulators for strongly correlated states of matter [1]. In particular, we describe the Mott-Superfluid transition of light in these systems and build a correspondence with the Bose- Hubbard model [2]. We also explore the possibilities of breaking time-reversal symmetry in such interacting photon systems [3] allowing to realize novel topological phases. Finally, we discuss the effect of interactions on two-dimensional topological (electron) band insulators [4].
[1] M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, Laser & Photonics Review 2, 527 (2008), and references therein.
[2] Jens Koch and Karyn Le Hur, Phys. Rev. A 80, 023811 (2009).
[3] Jens Koch, Andrew Houck, Karyn Le Hur & Steve Girvin, arXiv:1006.0762
[4] S. Rachel and Karyn Le Hur, Phys. Rev. B 82, 075106 (2010).Speaker: Karyn Le Hur (Yale University) -
19
Scaling and interaction-assisted transport in graphene with one-dimensional defectsI will discuss the scattering from one-dimensional defects in intrinsic graphene. It turns out that the Coulomb repulsion between electrons can induce singularities of such scattering at zero temperature like in one-dimensional conductors. In striking contrast to electrons in one space dimension, however, repulsive interactions here can enhance transport. I will present explicit calculations for the scattering from vector potentials that appear when strips of the material are under strain. There the predicted effects are exponentially large for strong scatterers.Speaker: Markus Kindermann (Georgia Institute of Technology)
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Lunch
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Afternoon free / Sightseeing
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20
Transient fluctuation relations for time-dependent particle transportIn this talk I consider transport in mesoscopic systems under the influence of time-varying driving forces, where fluctuation relations connect the statistics of pairs of time reversed evolutions of physical observables. I will discuss general functional fluctuation relations for current flow in mesoscopic quantum systems induced by time-varying forces. Successive measurement processes implied by this setup do not put the derivation of quantum fluctuation relations in jeopardy. While in many cases the fluctuation relation for a full time-dependent current profile may contain excessive information, a number of reduced relations can be given, and their application to mesoscopic transport will be discussed. Examples include the distribution of transmitted charge, where the derivation of a fluctuation relation requires the combined monitoring of the statistics of charge and work.Speaker: Reinhold Egger (Heinrich-Heine Universität, Düsseldorf)
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21
Strong coupling of single-electron tunneling to nanomechanical motionNanoscale resonators that oscillate at high frequencies are potentially exciting candidates for ultra-sensitive mass detectors, as well as for probing the mechanical motion of macroscopic objects in the quantum limit. Here, I will discuss our recent results studying a high-quality mechanical resonator made from a suspended carbon nanotube driven into motion by applying a periodic radio frequency potential using a nearby antenna. A high mechanical quality factor exceeding 10^5 allows the detection of a shift in resonance frequency caused by the addition of a single-electron charge on the nanotube. Single-electron charge fluctuations are found to induce periodic modulations of the mechanical resonance frequency. These single-electron “tuning” oscillations are a mechanical effect that is a direct consequence of single- electron tunneling oscillations. Additional evidence for the strong coupling of mechanical motion and electron tunneling is provided by an energy transfer to the electrons causing mechanical damping, and unusual nonlinear behavior induced by the single electron force. In the absence of external RF driving, we discover that a direct current through the nanotube spontaneously drives the mechanical resonator, exerting a force that is coherent with the high-frequency resonant mechanical motion.Speaker: Gary Steele (TU Delft)
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Coffee break
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22
Exchange cotunneling in quantum dots with spin-orbit couplingIn this talk I shall report on the effects of spin-orbit interaction (SOI) on the exchange cotunneling through a spinful Coulomb blockaded quantum dot. In the case of zero magnetic field, Kondo effect takes place via a Kramers doublet and the SOI will merely affect the Kondo temperature. In contrast, the breaking of time-reversal symmetry in a finite field has a marked influence on the effective Anderson, and Kondo models for a single level. The nonlinear conductance can now be asymmetric in bias voltage and may depend strongly on direction of the magnetic field. A measurement of the angle dependence of finite-field cotunneling spectroscopy thus provides valuable information about orbital, and spin degrees of freedom and their mutual coupling.
Reference: J. Paaske, A. Andersen, K. Flensberg, arXiv:1006.2371Speaker: Jens Paaske (NBI, Copenhagen) - 23
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Lunch
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24
Current correlations in the out-of-equilibrium interacting resonant level model.The exact knowledge of the density matrix for the self-dual interacting resonant level model in a steady state allows to compute the static current-current correlations. At zero temperature and in the limit of small voltage, the resulting shot noise reveals charge carriers with charge 2e, in agreement with the TBA description. This is confirmed by extensive time-dependent DMRG calculations.Speaker: Edouard Boulat (LMPQ, CNRS)
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25
Quantum phases of a supersymmetric model for lattice fermionsP. Fendley, K. Schoutens and J. de Boer introduced a class of models that, as a result of a judicious tuning of kinetic and potential terms, possess supersymmetry. In 1D this model is solved analytically and turns out to be quantum critical. The thermodynamic limit is described by an N=2 superconformal field theory. In 2D we typically find that the number of ground states grows exponentially with the area of the system. We call such systems superfrustrated. For certain 2D lattices, such as the square and octagon-square lattices, the growth is exponential in the linear size of the system. For the square lattice we present a remarkable relation between ground states and tilings. We will explain why we tentatively call the latter class of systems 'supertopological'.Speaker: Liza Huijse (University of Amsterdam)
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Coffee break
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26
Analogue models of gravity in Bose-Einstein condensatesThanks to the kinematical analogy between gravity and hydrodynamical systems, it will be possible to simulate in laboratory the behavior of some gravitational systems, and the associated quantum effects. Among them, the Hawking radiation for black holes, the quantum emission due to cosmological expansion, the dynamical Casimir effect -so far with no experimental data confirming their existence- could be observed in Bose- Einstein condensates in the near future. To this purpose, the crucial role played by the measurements of the quantum correlations associated to each effect is described.Speaker: Serena Fagnocchi (University of Nottingham)
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Bus transportation to the boat
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Conference dinner during the boat trip through the archipelago
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20
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Residual decoherence and manipulation of protected qubitsWe have shown how to implement protected qubits using some particular Josephson junction networks. The low energy physics of these systems is well described by the Kitaev toric code model, with proper boundary conditions ensuring the two-fold degeneracy of the ground-state. Using a generalized master equation approach, I will show that the decoherence times of such qubits are expected to grow exponentially with the system length, provided the spectral density of the noise is contained in a frequency interval smaller than the energy gap of the circuit. I will also describe how to implement single qubit rotations. A rather good surprise is that, in spite of the perturbation induced by the manipulation, some features of the topological protection remain effective. For instance, the rotation axis is itself protected with high accuracy against the effect of the environmental noise during the manipulation. A key role in these analyses is played by the non-local symmetries of such systems.Speaker: Benoit Doucot (LPTHE, CNRS)
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28
Josephson Junction Arrays for Quantum MetrologyThe one dimensional series Josephson Junction Array (JJA) is a rich system for the study of nonlinear dynamics and the quantum behavior of the superconducting phase. This talk will review some interesting features of JJA’s in several regimes: The regime of classical linear electrodynamics, where a mode structure is found that can be engineered to give microwave “photonic band gaps”. The regime of classical nonlinear electrodynamics, where JJA transmission lines can be used to realize parametric amplifiers. And the regime of strong quantum fluctuations of the phase, where a Coulomb blockade of Cooper pair tunneling can be realized which bares a striking duality to the classical DC Josephson effect. One objective of the study of this later regime, is to realize the dual to the AC Josephson effect, which could enable a new quantum standard of electrical current.Speaker: David Haviland (KTH)
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Coffee break
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Quantum Quenches in simple one-dimensional modelsQuantum quenches (i.e. a sudden variation of the parameter(s) of the Hamiltonian of a quantum system) will be addressed using the Luttinger and sine-Gordon models. For the latter, the exactly solvable Luther-Emery point as well as the semiclassical limit are analyzed. By computing the evolution of correlations following the quench, issues such as the lack of thermalization due to the large number of conserved quantities and the effect of quenching from a state for which correlations are characterized by a finite correlation length will be discussed.Speaker: Miguel Cazalilla (DIPC, San Sebastián)
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30
Quantum quenches in integrable and non-integrable systems: thermalization, locality and the role of many-body localization.I will describe recent studies of the dynamics of spin chains following a quench of one of the system parameters focusing on the characterization of relaxation and of the asymptotic state in relation to the integrability of the model. A detailed staudy of various model, such as the Quantum Ising and XXZ chains, suggests that for integrable system the behavior of two-point spin correlation functions shows that the correlators of operators that are non-local with respect to the quasiparticles of the model display an effective asymptotic thermal behavior. On the contrary, the two point correlation functions of operators that are local with respect to the quasiparticles do not behave thermally. A sufficiently strong integrability-breaking term, which induces thermalization to occur in general, both for local and non-local observables. I will discuss how this phenomenon is deeply rooted in a many-body localization/delocalization transition, i.e. is associated to a crossover/transition from localized to delocalized states in quasi-particle space.Speaker: Alessandro Silva (ICTP, Trieste)
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Lunch
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31
Quantum dynamics in ultracold atomic gasesSpeaker: Corinna Kollath (CPT, CNRS)
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32
Non-abelian anyons with ultracold atoms in artificial gauge potentialsUltracold atoms offer a useful tool to simulate the physics of the quantum Hall effect. In particular, non-abelian potentials acting on ultracold gases with two hyperfine levels can give raise to ground states with non-abelian excitations. We consider a realistic gauge potential for which the Landau levels can be exactly determined: the non-abelian part of the vector potential makes the Landau levels non- degenerate. In presence of strong repulsive interactions, deformed Laughlin ground states in general occur. However, at the degeneracy points of the Landau levels non-abelian quantum Hall states appear and explicit analytical results can be obtained.Speaker: Michele Burrello (SISSA)
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Coffee break
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33
Partition functions of non-Abelian Hall statesI present the derivation of partition functions of edge excitations for the best-known non-Abelian Hall states. I then discuss their use for describing experiments of Coulomb blockade and thermopower, and for determining entanglement entropies.Speaker: Andrea Cappelli (INFN, Firenze)
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