Quantum Matter in Low Dimensions: Opportunities and Challenges

30 Aug 2010, 08:00 → 24 Sept 2010, 18:00 Europe/Stockholm

132:028 (Nordita)

Eddy Ardonne (Nordita), Giuseppe Mussardo (Sissa, Italy), Henrik Johannesson (University of Gothenburg, Sweden)

The workshop is aimed at bringing together experts in the fields of nanoscale and low-dimensional condensed matter physics, quantum gases, integrable models, statistical and quantum field theory, and mathematical physics, to develop interdisciplinary communication and collaborations. Experimentalists will be visiting for shorter periods, to provide overview talks on recent developments. An important aspect of the workshop is to boost fundamental theoretical research on nanoscale and low-dimensional systems.

Problems that will be covered during the program are

• Theory for nanoscale devices for cold atoms (”atomic chips”)
• Development of Bethe Ansatz techniques to describe non-equilibrium and transport phenomena in low-dimensional systems
• Calculation of correlation functions in integrable quantum field theories and lattice models
• The study of disorder and interaction effects in topological insulators
• Theory for quantum phase transitions into topologically ordered states
• Correlation effects in graphene
• Interferometry of non-Abelian quantum Hall states
• Quantum impurities and entanglement in quantum information devices
• Conformal field theory and topological quantum computation

To apply for participation, please use the 'Application Form' in the menu on the left. The deadline for application is April 30, 2010. Decisions on participation will be made early in May, 2010.

From Monday, September 6th, till Friday, September 10, 2010, a conference, co-sponsored by INSTANS, will be held. Information about the conference, including a list of invited speakers, as well as a registration page, can be found on the conference website .

Monday 30 August

Intorductory meeting with coffe and cakes

Wednesday 1 September

1 Topological Entanglement in Fractional Quantum Hall Excitation Eigenstates

Zlatko Papic: Entanglement in topological ordered states has so far been investigated through the perspective of the ground-state wave function. By presenting entanglement spectra of the (quasihole) excitations of fractional quantum Hall states, I will show their typical structure in Abelian, as well as non- Abelian cases of the Read-Rezayi sequence, including the realistic Coulomb-interaction ground states that they are believed to describe. I will argue that the excitation wave functions contain sufficient information to identify the system's topological order.

Speaker: Zlakto Papic (Institute of Physics)

Thursday 2 September

2 Commensurability effects caused by the modulated spin-orbit interaction in one-dimensional electron liquids

(with H. Johannesson, M. Malard and H. Strom)

Speaker: Gia Japaridze (Andronikashvili Institute of Physics)

3 Narrow-gap semiconductors with strong Coulomb repulsion

Speaker: Vadim Cheianov (Lancaster University)

Friday 3 September

4 Breaking integrability and confinement in 2d statistical models

Speaker: Giuseppe Mussardo (SISSA)

5 Extended global symmetry of the Hubbard model on bipartite lattices

J. M. P. Carmelo, Stellan Östlund, and M. J. Sampaio The Hubbard model on a bipartite lattice is one of the most studied many- particle quantum problems. However, except in one dimension the model has no exact solution and there remain many open questions about its properties. Here we report a recent exact result [1]. According to it, for on-site interaction U 6= 0 the local SU(2) × SU(2) × U(1) gauge symmetry of the Hubbard model on a bipartite lattice with vanishing transfer integral t = 0 studied in [2] can be lifted to a global [SU(2)× SU(2)× U(1)]/Z2 2 = SO(3) ×SO(3) ×U(1) symmetry in the presence of the kinetic-energy hopping term of the Hamiltonian with t > 0. The generator of the new found hidden independent charge global U(1) symmetry, which is not related to the ordinary U(1) gauge subgroup of electromagnetism, is one half the rotated- electron number of singly-occupied sites operator. Although addition of chemicalpotential and magnetic-field operator terms to the model Hamiltonian lowers its symmetry, such terms commute with it. Therefore, its energy eigenstates refer to representations of the new found global SO(3) × SO(3) × U(1) = [SO(4) × U(1)]/Z2 symmetry, which is expected to have important physical consequences. Our studies reveal that for U/4t > 0 the model charge and spin degrees of freedom are associated with U(2) = SU(2) × U(1) and SU(2) symmetries [1], respectively, rather than with two SU(2) symmetries. (The latter case would hold if the model global symmetry was only SO(4) = [SU(2) ×SU(2)]/Z2.) The occurrence of such charge U(2) = SU(2) × U(1) symmetry and spin SU(2) symmetry is for the onedimensional model behind the different ABCDF and ABCD forms of the charge and spin monodromy matrices, respectively, found by the inverse scattering method exact solution [3].
1. J.M.P. Carmelo, Stellan Östlund, and M.J. Sampaio, Ann.Phys. 325, 1550 (2010).
2. Stellan Östlund and Eugene Mele, Phys.Rev. B 44, 12413 (1991).
3. M.J. Martins and P.B. Ramos, Nucl.Phys. B 522, 413 (1998).

Speaker: Jose Carmelo (Department of Physics, University of Minho)

Slides 2010-09-03-carmelo.pdf

6 What can graphene teach us about the bridge between quantum field theory and kinetic theory?

Semiclassical spin-coherent kinetic equations can be derived from quantum theory with many different formalisms. For 2d Dirac electrons (e.g. in graphene, 3d topological insulators, ...) we found to our surprise that well established formalisms give different results. We have been able to point out the exact source of the discrepancy and raise fundamental questions about how to derive semiclassical kinetic equation when some quantum coherence must be retained. Further, in monolayer graphene we make the unintuitive finding that there could be finite electron-hole coherent quantum effects even far away from the point where electron and hole bands touch.

Speaker: Janik Kailasvuori (MPIPKS (Dresden))

Slides 2010-09-03-kailasvuori.pdf

Monday 13 September

7 Exciton Hierarchies in Carbon Nanotubes

I present evidence that the strong electron-electron interactions in gapped carbon nanotubes lead to finite hierarchies of excitons within a given nanotube subband. I study these hierarchies by employing a field theoretic reduction of the gapped carbon nanotube permitting electron-electron interactions to be treated exactly. I analyze this reduction by employing a Wilsonian-like numerical renormalization group. I am so able to determine the gap ratios of the one-photon excitons as a function of the effective strength of interactions. I also determine within the same subband the gaps of the two-photon excitons, the single particle gaps, as well as a subset of the dark excitons. The strong electron-electron interactions in addition lead to strongly renormalized dispersion relations where the consequences of spin-charge separation can be readily observed.

Speaker: Robert Konik (Brookhaven National Lab)

Slides 2010-09-13-1-Konik.pdf

Tuesday 14 September

8 Entanglement in Fractional Quantum Hall states

We present a new approach for obtaining the scaling behavior of the entanglement entropy in fractional quantum Hall (FQH) states from finite-size wavefunctions. By employing the torus geometry and the fact that the torus aspect ratio can be readily varied, we can extract the entanglement entropy of a spatial block as a continuous function of the block boundary length. This approach allows us to extract the topological entanglement entropy with an accuracy superior to that possible for the spherical or disc geometry, where no natural continuously variable parameter is available. Other than the topological information, the study of entanglement scaling is also useful as an indicator of the difficulty posed by FQH states for various numerical techniques. We also analyze the entanglement spectrum of Laughlin states on the torus and show that it is arranged in towers, each of which is generated by modes of two spatially separated chiral edges. This structure is present for all torus circumferences, which allows for a microscopic identification of the prominent features of the spectrum by perturbing around the thin- torus limit.

Speaker: Emil Bergholtz (Max Planck Institute for the Physics of Complex Systems)

Slides 2010-09-14-1-Bergholtz.pdf

Wednesday 15 September

9 Theory Seminar: Threshold Singularities in the 1D Hubbard Model

I consider the single-particle spectral function of the one dimensional Hubbard model below half-filling. For fixed momentum the spectral function exhibits kinematic thresholds as a function of energy. Above these thresholds the spectral function exhibits power-law singularities. I determine the threshold exponent, which is momentum dependent and differs from the Luttinger liquid prediction. The difference arises from irrelevant perturbations to the low-energy Luttinger liquid description.

Speaker: Fabian Essler (Oxford University)

10 Unusual singular behavior of the entanglement entropy in one dimension

We study the bipartite entanglement entropy for one- dimensional systems. Its qualitative behavior is quite well understood: for gapped systems the entropy saturates to a finite value, while it diverges logarithmically as the logarithm of the correlation length as one approaches a critical, conformal point of phase transition. Using the example of two integrable models, we argue that close to non-conformal points the entropy shows a peculiar singular behavior, characteristic of an essential singularity. At these non-conformal points the model undergoes a discontinuous transition, with a level crossing in the ground state and a quadratic excitation spectrum. We propose the entropy as an efficient tool to determine the discontinuous or continuous nature of a phase transition also in more complicated models.
- F. Franchini, A. R. Its, B.-Q. Jin, V. E. Korepin; J. Phys. A: Math. Theor. 40 (2007) 8467-8478
- F. Franchini, A. R. Its, V. E. Korepin; J. Phys. A: Math. Theor. 41 (2008) 025302
- F. Franchini, E. Ercolessi, S. Evangelisti, F. Ravanini; arXiv:1008.3892

Speaker: Fabio Franchini (SISSA)

Slides 2010-09-15-1-Franchini.pdf

Thursday 16 September

11 Numerical Study of Localized Quasiholes at nu=5/2 and the Majorana Fermion

We discuss new results of exact diagonalizations of electron systems with localized quasiholes at ν = 5/2 for interactions varying between the pure Coulomb interaction and the 3-body interaction for which the Moore-Read state is the exact ground state.

Speaker: Rudolf Morf (Condensed Matter Theory Group, Paul Scherrer Institute, Villigen, Switzerland)

Slides 2010-09-16-1-Morf.pdf

Friday 17 September

12 New exact results on lattice models with the Kitaev interactions

Speaker: Jiri Vala (National University of Ireland Maynooth)

Slides 2010-09-17-1-Vala.pdf

Monday 20 September

13 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).

Speaker: Jenia MOZGUNOV (Landau Institute for Theoretical Physics)

Paper 2010-09-20-1-Mozgunov.pdf

Tuesday 21 September

14 Confinement in Ising field theory and Ising spin chain: Bethe-Salpeter equation approach

The kink topological excitations are quite common in the two dimensional field theories with Hamiltonian invariant under some discrete symmetry group. If such symmetry is spontaneously broken in the ordered phase, the latter has a discrete set of degenerate vacuums. The kinks separating two different vacuums behave like stable quantum particles which can propagate in the system. Adding a small interaction, which explicitly breaks the Hamiltonian symmetry, lifts the degeneracy of ground states and leads to confinement of kinks. This simple scenario of confinement is realized in many two dimensional models. I review recent progress in understanding of the kink confinement in the quantum Ising spin chain, and in its continuum limit - Ising field theory, which correspond to the symmetry group Z2. This progress has been achieved due to the Bethe-Salpeter equation approach introduced by Fonseca and Zamolodchikov.

Speaker: Sergei RUTKEVICH (Institute of Solid State and Semiconductor Physics)

Slides 2010-09-21-1-Rutkevich.pdf

Wednesday 22 September

15 Theory seminar: Probing non-Abelian statistics with quantum Hall interferometry

Topologically ordered phases of matter have recently become a focus of much attention, both theoretical and experimental. In two spatial dimensions such phases may support anyons – quasiparticles that are neither bosons nor fermions. Moreover, anyons with non-Abelian statistics can occur, particularly in the fractional quantum Hall regime. In this talk, I will focus on solid state interferometers designed to detect such exotic statistics. I will discuss recent experiments in the the quantum Hall regime at 5/2 filling where the evidence for the existence of non-Abelian anyons may have in fact been observed for the first time. I will also mention potential applications of such interferometeric schemes for topological quantum computation.

Speaker: Kirill Shtengel (University of California, Riverside)

Slides 2010-09-22-1-Shtengel.pdf

16 Universal results for 2D percolation from quantum field theory

Speaker: Gesualdo Delfino (SISSA)

Slides 2010-09-22-2-Delfino.pdf