Opening of the conference

• Lárus Thorlacius and scientific coordinators

Five years of INSTANS

• Giuseppe Mussardo (SISSA, Chair of INSTANS steering committee)

Graphene: relativistic electrons in carbon flatland

• Eva Andrei (Rutgers University)

The 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.<br /> G. Li, A. Luican and E. Y. Andrei, Phys. Rev. Lett 102, (2009).

Strains and gauge fields in graphene

• Francisco Guinea (CSIC, Madrid)

Lattice 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.<br /> [1] A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, Rev. Mod. Phys. 81, 109 (2009)<br /> [2] M. A. H. Vozmediano, M. I. Katsnelson, F. Guinea, Phys. Rep., in press (2010). <br /> [3] F. Guinea, M. I. Katsnelson, A. K. Geim, Nature Phys. 6, 30 (2010). <br /> [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).

Magnetism and superconductivity in graphene from electronic correlations.

• Annica Black-Schaffer (Nordita)

TBA

Cold atoms in 1D in and out of equilibrium

• David Weiss (Pennsylvania State University)

TBA

Quantum critical behavior in driven and strongly interacting Rydberg gases

• Hans Peter Büchler (Universität Stuttgart)

We 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.

Competing orders in one-dimensional multicomponent cold fermions

• Philippe Lecheminant (LPTM, Université de Cergy-Pontoise)

We 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.

Majorana-Shockley states in topological superconductors

• Carlo Beenakker (Leiden University)

Vortices 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.

Quantum Imaging of Topologically Ordered Matter

• Hari Manoharan (Stanford University)

Deforming 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.

Quantum magnetism and interaction effects in topological insulators

• Gregory Fiete (University of Texas, Austin)

We 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.

Fermion transfer by vortex tunneling

• Johan Nilsson (University of Gothenburg)

We 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.

Dynamics of one-dimensional correlated systems with and without disorder

• Joel Moore (University of California, Berkeley)

Correlated 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").

Entanglement entropy of disconnected regions in extended systems

• Pasquale Calabrese (Universita' di Pisa)

The 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.

Hierarchy of edge-locking effects in interacting 1D lattice systems

• Masudul Haque (MPI-PKS Dresden)

In one-dimensional lattices with open boundaries, I will present a `fractal' structure high up in the energy specturm, and associated out-of-equilibrium consequences. <br /> The non-equilibrium consequences are a hierarchy of `edge-locking' effects. <br /> I will show versions of the phenomenon for three classic condensed-matter models:<br /> (1) the Bose-Hubbard model;<br /> (2) the spinless fermion model with nearest-neighbor repulsion;<br /> (3) the XXZ (Heiseberg-Ising) spin chain.

Incompressibility, quantum geometry, and Hall viscosity in the FQHE

• Duncan Haldane (Princeton University)

Most 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.

Pfaffian vs AntiPfaffian

• Steven Simon (University of Oxford)

Novel Phases: From Photons to Electrons

• Karyn Le Hur (Yale University)

Recently, 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].<br /> [1] M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, Laser & Photonics Review 2, 527 (2008), and references therein.<br /> [2] Jens Koch and Karyn Le Hur, Phys. Rev. A 80, 023811 (2009).<br /> [3] Jens Koch, Andrew Houck, Karyn Le Hur & Steve Girvin, arXiv:1006.0762<br /> [4] S. Rachel and Karyn Le Hur, Phys. Rev. B 82, 075106 (2010).

Scaling and interaction-assisted transport in graphene with one-dimensional defects

• Markus Kindermann (Georgia Institute of Technology)

I 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.

Transient fluctuation relations for time-dependent particle transport

• Reinhold Egger (Heinrich-Heine Universität, Düsseldorf)

In 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.

Strong coupling of single-electron tunneling to nanomechanical motion

• Gary Steele (TU Delft)

Nanoscale 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.

Exchange cotunneling in quantum dots with spin-orbit coupling

• Jens Paaske (NBI, Copenhagen)

In 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.<br /> Reference: J. Paaske, A. Andersen, K. Flensberg, arXiv:1006.2371

Non-equilibrium transport through double quantum dot devices: A non-Fermi liquid critical point

• Eran Sela (UBC, Vancouver)

Current correlations in the out-of-equilibrium interacting resonant level model.

• Edouard Boulat (LMPQ, CNRS)

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.

Quantum phases of a supersymmetric model for lattice fermions

• Liza Huijse (University of Amsterdam)

P. 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'.

Analogue models of gravity in Bose-Einstein condensates

• Serena Fagnocchi (University of Nottingham)

Thanks 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.

Residual decoherence and manipulation of protected qubits

• Benoit Doucot (LPTHE, CNRS)

We 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.

Josephson Junction Arrays for Quantum Metrology

• David Haviland (KTH)

The 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.

Quantum Quenches in simple one-dimensional models

• Miguel Cazalilla (DIPC, San Sebastián)

Quantum 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.

Quantum quenches in integrable and non-integrable systems: thermalization, locality and the role of many-body localization.

• Alessandro Silva (ICTP, Trieste)

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.

Quantum dynamics in ultracold atomic gases

• Corinna Kollath (CPT, CNRS)

Non-abelian anyons with ultracold atoms in artificial gauge potentials

• Michele Burrello (SISSA)

Ultracold 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.

Partition functions of non-Abelian Hall states

• Andrea Cappelli (INFN, Firenze)

I 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.