Workshop
New quantum states of matter in and out of equilibrium
Apr 10, 2012  Jun 01, 2012During the last decade a host of experiments has established the existence of highly unconventional states of matter in a variety of low dimensional quantum systems. These include equilibrium states characterized by topological properties as well as stationary states in out of equilibrium situations. Both of these give access to hitherto unexplored areas of manybody quantum physics. This research workshop will bring together experts in these areas, which have witnessed compelling advances during the last few years. .
There will be a conference on 2125/05/2012
Topics
 Topological phases of matter
 NonAbelian Statistics
 Topological Insulators
 Tensor network states
 Quantum quenches
 Transport in nanostructures
 Cold atomic gases
 Entanglement in extended systems
Organizers
Ian Affleck (University of British Columbia), Pasquale Calabrese (Pisa University),
John Cardy (University of Oxford), Fabian H. L. Essler (University of Oxford),
Eduardo Fradkin (University of Illinois at UrbanaChampaign),
F. Duncan M. Haldane (Princeton University).
Local organizer
Marco Tarlini
Contact
calabres@df.unipi.it
Related events
New quantum states of matter in and out of equilibrium  Conference (Conference)  May 21, 2012
Talks
Date  Speaker  Title  Type  Useful Links  

Apr 11, 2012  11:00  Ehud Altman  Real space RG for dynamics of random spin chains and manybody localization  Seminar 
Abstract
Real space RG for dynamics of random spin chains and manybody localization Using a novel renormalization group scheme formulated in real time I will give an asymptotically exact description of the long time evolution of a random XXZ spin1/2 chain undergoing a quantum quench. I will show that for sufficiently strong disorder the system dynamically \\\"flows\\\" to a localized infinite randomness fixed point. This result demonstrates the existance of a manybody localized state of interacting fermions or bosons in 1d. We show that particle number fluctuatons in this state are essentially localized. On the other hand the entanglement entropy grows without bound but saturates in any finite chain to a value significantly smaller than it would be had the system reached thermal equilibrium. Finally I will give a criterion for the basin of attraction of the infinite randomness fixed point. Based on this criterion we conjecture a line (disorder strength versus interaction strength) marking the manybody localization transition. 
Slides  
Apr 12, 2012  11:30  Nigel Cooper  Topological Bandstructures for Ultracold Atoms  Seminar 
Abstract
Topological Bandstructures for Ultracold Atoms One of the most important techniques in the ultracold atom toolbox is the optical lattice: a periodic scalar potential formed from standing waves of light. Optical lattices are central to the use of atomic gases as quantum simulators, and allow the exploration of strongcorrelation phenomena related to condensed matter systems. In this talk, I shall describe how simple laser configurations can give rise to a new kinds of optical lattice in which the bands have nontrivial topological character. First, I shall describe how coherent optical dressing can cause atoms to experience a periodic effective magnetic flux with high mean density. The resulting bandstructure has narrow energy bands with nonzero Chern numbers, analogous to the Landau levels of a charged particle in a uniform magnetic field. I shall then describe how this idea can be generalized to form bands with nontrivial Z_2 invariant in 2D and 3D. 
Slides  
Apr 13, 2012  11:30  Jesper Jacobsen  Exact corner free energies for twodimensional integrable lattice models  Seminar 
Abstract
Exact corner free energies for twodimensional integrable lattice models We obtain long series expansions for the bulk, surface and corner free energies for several twodimensional statistical models. The models encompass all integrable curves of the Qstate Potts model on the square and triangular lattices, including the antiferromagnetic transition curves and the Ising model (Q=2) at temperature T, as well as a fullypacked O(n) type loop model on the square lattice. All expansions turn out to have the form of infinite products with a certain periodicity property, enabling us to conjecture the form of the expansions to all orders. We analyze in detail the limits in which the models become critical. In this limit the divergence of the corner free energy defines a universal term which can be compared with the conformal field theory (CFT) predictions of Cardy and Peschel. This allows us to deduce the asymptotic expressions for the correlation length in several cases. 
Slides  
Apr 16, 2012  11:30  Roderich Moesnner  Disorder and dynamics in Kitaev's spin liquids  Seminar  
Apr 17, 2012  11:30  Didier Poilblanc  Entanglement spectrum and boundary theories using PEPS  Seminar 
Abstract
Entanglement spectrum and boundary theories using PEPS In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated to their boundaries have been observed. Here I discuss how an exact duality mapping between the bulk of a quantum spin system and its boundary can be provided using Projected Entangled Pair States (PEPS). For a bipartition, the entanglement spectrum can be related to the spectrum of a boundary Hamiltonian acting on emerging edge degrees of freedom. This is illustrated in the case of simple twodimensional systems such as (deformed) AKLT and topological SU(2)invariant RVB states. In the later case, I shall describe how the topological character of the wavefunction (a Z_2 liquid on the kagome lattice) is reflected on the structure of the corresponding boundary Hamiltonian. 
Slides  
Apr 17, 2012  16:30  F. Burnell  Fractional topological insulators  Informal seminar 
Abstract
Fractional topological insulators Topological band insulators are phases of matter with gapless edge modes that are protected by timereversal symmetry. I will discuss the conditions under which similar phases can exist in strongly interacting, fractional systems. I will also review our present understanding of field theoretic approaches to these systems. 

Apr 18, 2012  11:30  German Sierra  Quantum spin models in one and two dimensions from the WZW model  Seminar 
Abstract
Quantum spin models in one and two dimensions from the WZW model CFT has two well known applications. It describes the low energy physics of critical spin chains and it also provides a toolbox for constructing wave functions for Fractional Quantum systems, such as the Laughlin and MooreRead. In this talk, we shall unify these two applications in the framework of spin systems. In this realm we shall discuss the HaldaneShastry model in 1D and the KalmeyerLaughlin model in 2D, providing several generalizations of them. 
Slides  
Apr 18, 2012  16:30  J. Dubail  Topological phases of matter: from bulk model wave functions to the edge theory  Informal seminar 
Abstract
Topological phases of matter: from bulk model wave functions to the edge theory
After an introduction to the formalism of trial wave functions
given by conformal blocks (the socalled \"MooreRead construction\"),
I will discuss how the edge excitations emerge from these
bulk wave functions. I will illustrate this formalism with a few examples
(p+ip superconductors and some fractional quantum Hall states).
If I have enough time, I will also discuss the entanglement spectra
of these states.

Slides  
Apr 19, 2012  11:30  Robert Raussendorf  The computational power of AKLT states  Seminar 
Abstract
The computational power of AKLT states
In this talk I pursue a perhaps somewhat unfamiliar question: What is the computational power of quantum states? 
Slides  
Apr 19, 2012  16:30  E. Tonni  Entanglement entropy: Insights from the two intervals case.  Informal seminar 
Abstract
Entanglement entropy: Insights from the two intervals case.
While the entanglement entropy for one interval in two dimensional CFT is sensible only to the central charge, in the case of many intervals it includes the full operator content of the theory. We make this statement manifest through an OPE expansion valid for any CFT. This general result is tested quantitatively in the case of two intervals for the compactified boson and for the Ising model, where the expressions of the Renyi entropies are derived in terms of Riemann theta functions and checked against numerical data obtained from spin chains. 
Slides  
Apr 20, 2012  11:30  K. Schoutens  NonAbelian spin textures  Seminar 
Abstract
NonAbelian spin textures
We present the following results for spinfull excitations over the
MooreRead quantum Hall state. 

Apr 20, 2012  16:30  L. Tagliacozzo  Simulation of Dynamical Abelian gauge fields with optical lattices  Informal seminar 
Abstract
Simulation of Dynamical Abelian gauge fields with optical lattices
We discuss how to implement the simulation of dynamical Abelian gauge
theories on optical lattices .
We will follow a constructive derivation of LGT that will uncover
which are the necessary the three main ingredients one needs to
implement in experiments. 
Slides  
Apr 23, 2012  11:30  Benjamin Doyon  Heat flow in nonequilibrium steady states from CFT  Seminar 
Abstract
Heat flow in nonequilibrium steady states from CFT Let two large quantum systems prepared at different temperatures come into contact and evolve unitarily. After a large enough time, a nonequilibrium steady state will exist whereby energy flows from one system to the other. I will explain how to describe the steady state in the universal region near quantum critical points, using concepts of quantum field theory. I will then describe exact results from Conformal Field Theory for the energy current and its fluctuations (all largetime energytransfer cumulants). This is based on works with Denis Bernard. 
Slides  
Apr 24, 2012  11:30  Roberto Bondesan  Edge states at the spin quantum Hall transitions 
Abstract
Edge states at the spin quantum Hall transitions I discuss edge states in quantum network models describing Anderson transitions separating different phases of topological insulators. For the case of the spin quantum Hall effect (class C), some transport properties map to a classical localization problem formulated in terms of a loop model. We determine exact critical exponents governing the decay of the conductance at higher plateaus transitions, and our prediction are found to be in very good agreement with numerical simulations. 
Slides  
Apr 25, 2012  11:30  Michael Tomka  Geometric phase contribution to quantum nonequilibrium manybody dynamics  Seminar 
Abstract
Geometric phase contribution to quantum nonequilibrium manybody dynamics In this talk I will study the influence of the geometry of a quantum systems underlying space of states on its quantum manybody dynamics. I will show that there is an interplay between dynamical and topological ingredients of quantum nonequilibrium dynamics. This interplay is illustrated on the example system of the anisotropic XY ring in a transverse magnetic field where in addition all the spins are rotated around the axis of the applied magnetic field. In particular, if the rotation velocity is slow, nonadiabatic transitions in the dynamics are dominated by the dynamical phase. In the opposite limit geometric phase strongly affects transition probabilities. This interplay can lead to a nonequilibrium phase transition between these two regimes. 
Slides  
Apr 26, 2012  11:30  Ettore Vicari  Classical and quantum critical behaviors in trapped particle systems  Seminar 
Abstract
Classical and quantum critical behaviors in trapped particle systems
Recent experiments on the BoseEinstein condensation in dilute atomic
vapors and atom systems in optical lattices have provided a great
opportunity to investigate the interplay between quantum and
statistical behaviors in particle systems. In these systems, phase
transitions with their quantum and thermal critical behaviors are
phenomena of great interest. A common feature of these experimental
realizations is the presence of a trapping potential coupled to the
particle density. Therefore, a theoretical description of how
criticality develops in the presence of the confining enternal field
is of great importance for experiments. 
Slides  
Apr 26, 2012  16:30  Olalla Castro Alvaredo  Entanglement Entropy of Degenerate Ground States: Permutation Symmetric States  Seminar  Slides  
Apr 27, 2012  11:30  Raoul Santachiara  Wavefunctions and dualities in the "nonAbelian" sector of the CalogeroSutherland model  Seminar 
Abstract
Wavefunctions and dualities in the "nonAbelian" sector of the CalogeroSutherland model The CalogeroSutherland model is a 1D quantum model describing long range interacting particles. The (classical and) quantum CalogeroSutherland systems have been proven to be completely integrable and the algebraic structures responsible for the solvability of these models have appeared in various area of theoretical physics. We will review these structures and we will point out the existence and the properties of a new family of wavefunctions which are given by CFT conformal blocks. We will be discuss how the well known duality of the model manifests in these sectors. Finally we will point out the strict relation between these results, the integrable structure of the CFT and the celebrated AGT conjecture relating 2D CFT to 4D supersymmetric gauge theories. 

Apr 30, 2012  11:30  Giacomo Roati  Fermi(ons) back to Florence  Seminar 
Abstract
Fermi(ons) back to Florence
Ultracold atoms are ideal quantum simulators [1] due to the unprecedented possibility of con trolling the relevant physical parameters. Infact they are perfect environments where to implement quantum models and where to study condensed matter problems [2]. In this seminar, I will describe the new experiment at LENS dedicated to the study of degener ate atomic Fermi gases. In particular, in this new setup, we aim at simulating twodimensional stronglycorrelated layered fermions. These systems show remarkable physical properties due to the combination of statistics, interactions and dimensionality. Paradigmatic examples are highTc superconductors.
We plan to investigate different 2D geometries (single and weakly coupled layers) also in the pres ence of a controllable disorder [3]. We will address the role of layering by studying the interlayers Josephson tunneling, that will be a tool to measure the superfluid energy gap. The disorder will be introduced on the layers by imprinting speckle patterns, simulating in this way the physics of granular superconductors. In these systems, a superfluid to insulator transition is observed for critical values of disorder [4].
We also plan to implement quantum FermiHubbard Hamiltonians by superimposing optical lat tices on the layers. These models are expected to unveil the physics of highTc superconductors. In particular, we want to simulate the attractive FermiHubbard model whose rich phenomenology should be more accessible in the experiment [5].


Apr 30, 2012  16:30  Vincenzo Alba  Entanglement spectrum in quantum many body systems  Seminar 
Abstract
Entanglement spectrum in quantum many body systems The entanglement between two parts of a manybody system can be characterized in detail by the entanglement spectrum. Focusing on gapped phases of onedimensional systems, I will show how this spectrum is dominated by contributions from the boundary between the parts. The boundarylocal nature of the entanglement spectrum is clarified through its hierarchical level structure, through the combination of two singleboundary spectra to form a twoboundary spectrum, and through consideration of dominant eigenfunctions of the entanglement Hamiltonian. Finally I will discuss the main properties of the entanglement spectrum of the two dimensional Bose Hubbard model in both the superfluid and the Mott insulating phase. 
Slides  
May 02, 2012  11:30  Andrea Trombettoni  Quantum simulations with ultracold atoms  Seminar 
Abstract
Quantum simulations with ultracold atoms In this talk I will present two examples of quantum simulations with ultracold atoms. In the first part I discuss the properties of ultracold gases with two hyperfine levels in nonabelian potential. We consider a gauge potential for which the Landau levels can be exactly determined: the nonabelian part of the vector potential makes the Landau levels nondegenerate. In the presence of strong repulsive interactions, deformed Laughlin ground states occur in general. However, at the degeneracy points of the Landau levels, nonabelian quantum Hall states may appear. In the second part I will discuss anisotropic GinzburgLandau and LawrenceDoniach models describing a layered superfluid ultracold Fermi gas in optical lattices. We derive the coefficients of the anisotropic GinzburgLandau and the mass tensor as a function of anisotropy, filling and interaction, showing that near the unitary limit the effective anisotropy of the masses is significantly reduced. The anisotropy parameter is shown to vary in realistic setups in a wide range of values. We also derive the LawrenceDoniach model  often used to describe the 2D3D dimensional crossover in layered superconductors  for a layered ultracold Fermi gas, obtaining a relation between the interlayer Josephson couplings and the GinzburgLandau masses. A discussion of effective models for the dynamics of Fermi gases in layered optical lattices is as well presented. 
Slides  
May 03, 2012  11:30  Vincent Pasquier  Some remarks on the Hall effect.  Seminar 
Abstract
Some remarks on the Hall effect. I will discuss some problems in the Hall effect, and possible connection to intergrability, in particular Benjamin Ono and W_infty. I will illustrate them in the case of the so called Hall viscosity. 

May 03, 2012  16:30  Antonello Scardicchio  Anderson localization in strongly interacting systems: a case study  Seminar 
Abstract
Anderson localization in strongly interacting systems: a case study We study the interplay of Anderson localization and strong interactions in a disordered spin chain, showing that sufficiently strong interaction can restore ergodicity of the system in line with the recently advanced manybody localization transition conjecture. 

May 04, 2012  11:30  Nicole Fabbri  Investigating the momentum distribution of 1D quasicondensates  Seminar 
Abstract
Investigating the momentum distribution of 1D quasicondensates The dynamical structure factor S(q,ω) provides an important depiction of the dynamic behavior of quantum manybody systems. For gaseous BoseEinstein condensates, it allows a fully characterization of the excitation, providing information on both the collective excitations and the momentum distribution. In cold atoms experiments, S(q, ω) can be measured via inelastic lightscattering (Bragg spectroscopy), that couples two momentum states of the same internal groundstate by a stimulated twophotons transition. In this work, we have characterized onedimensional chains of bosons in the quasicondensate regime, realized by loading a BoseEinstein condensate of Rb87 in a pair of orthogonal reddetuned optical lattices. In the first part of the talk, I will present the results of Bragg experiments on this system: We have studied its response to excitations with high momentum transfer q, which reflects the initial momentum distribution, dominated by phase fluctuations. Measuring the excitation spectra of the 1D gases for different lattice depths, we have observed an enlargement of the width of those spectra, revealing a reduction of the coherence length of the system. Then, I will show that timeofflight absorption imaging can be used as alternative simple probe to directly measure the coherence length of onedimensional gases in the regime where phase fluctuations are strong [1]. This method is suitable for future studies such as investigating the effect of disorder on the phase coherence. [1] N. Fabbri, D. ClĂ©ment, L. Fallani, C. Fort, and M. Inguscio, Physical Review A 83, 031604(R) (2011). 
Slides  
May 07, 2012  11:30  Leonardo Fallani  Twoelectron Quantum Gases in Florence  Seminar 
Abstract
Twoelectron Quantum Gases in Florence We will present the LENS experimental activity on quantum degenerate twoelectron atoms. We will report on the recent production of ytterbium BoseEinstein condensates and illustrate the possibilities that are offered by this system for quantum simulation and quantum information experiments. 
Slides  
May 08, 2012  11:30  M. Joe Bhaseen  Exploiting AdS/CFT Far From Equilibrium  Seminar 
Abstract
Exploiting AdS/CFT Far From Equilibrium Recent developments highlight the potential role of the AdS/CFT correspondence in condensed matter physics. We discuss the application of these techniques to strongly correlated systems far from equilibrium. 

May 09, 2012  16:30  Andrew James  Entanglement entropy and spectra in 2D quantum systems through arrays of coupled chains.  Seminar  
May 10, 2012  11:30  Vladimir Gritsev  Dynamical deviation from integrability: quantum version of KAM  Seminar  
May 11, 2012  11:30  Reinhold Egger  Electronic transport through topological insulators  Seminar 
Abstract
Electronic transport through topological insulators
In this talk, I will discuss (a) the helical Luttinger liquid realized in nanowires made of
3D topological insulators [1] and (b) transport through Majorana fermion states in the
presence of Coulomb blockade effects [2]. 
Slides  
May 14, 2012  11:30  Francesco Minardi  Dynamics of impurities in a onedimensional Bose gas  Seminar 
Abstract
Dynamics of impurities in a onedimensional Bose gas
In a recent experiment [1], we have used a largely imbalanced mixture of K41 and Rb87 to create impurities in a onedimensional gas of bosons. The impurity K41 atoms, initially localized by means of a speciesselective optical potential, were abruptly released and let expand and oscillate in the onedimensional harmonic potential, while interacting with the surrounding bath of Rb87 atoms. Thanks to Feshbach resonances, modified by the confinement, we have adjusted the interspecies coupling constant, g1d, between impurity and bath. We observed a clearcut dependence of the amplitude of the oscillations on g1d, whereas the oscillation frequency was independent on g1d within experimental uncertainties.
While a conclusive explanation is still lacking, we propose a theoretical analysis that, under simplifying approximations, captures the main features of the experimental findings in terms of a polaronic massshift model formulated following Feynman variational method [2]. 
Slides  
May 15, 2012  11:30  Ady Stern  From fractionalized topological insulators to fractionalized Majoranas  Seminar  Slides  
May 16, 2012  11:30  Ian Affleck  Magnetism on the edges of graphene ribbons  Seminar 
Abstract
Magnetism on the edges of graphene ribbons One of the many fascinating properties of graphene is the existence of gapless edge states for ribbons with zigzag edges, in a noninteracting approximation. It has been argued, mainly based on mean field theory, that the edge electrons become ferromagnetically polarized when interactions are included. I will take some steps towards a rigorous proof of this conjecture for the weak coupling Hubbard model on the honeycomb lattice and analyse an important perturbation which can eventually destroy the magnetic moment. 
Slides  
May 17, 2012  11:30  Michael Pustilnik  Relaxation of a highenergy quasiparticle in a 1D Bose liquid  Seminar  Slides  
May 18, 2012  11:30  Andrea Gambassi  Dynamic correlations, fluctuationdissipation relations and effective temperatures after a quantum quench of the Ising chain  Seminar 
Abstract
Dynamic correlations, fluctuationdissipation relations and effective temperatures after a quantum quench of the Ising chain Fluctuationdissipation relations and effective temperatures have been successfully used to describe the nonequilibrium behavior of classical system and quantum glasses in contact with thermal baths. We extend this approach to quantum isolated manybody systems after a global quench in some of the parameters of the corresponding hamiltonians. The possible emergence of an eventual thermal behavior can be tested by studying the relation between dynamic correlation and response functions in the stationary regime. In fact, the various effective temperatures defined on the basis of these dynamical quantities have to coincide if thermalization within the Gibbs ensemble occurs. We explore this issue by considering the quantum Ising chain after a critical quench of the transverse field. In spite of some deceptive quantity, the lack of Gibbs thermalization is apparent within this general approach. 
Slides  
May 29, 2012  11:30  Frank Pollmann  Detection of Symmetry Protected Topological Phases in 1D  Seminar 
Abstract
Detection of Symmetry Protected Topological Phases in 1D A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped, symmetric phases in 1D systems can be completely characterized using tools related to projective representations of the symmetry groups. An example of a symmetry protected topological phase is the Haldane phase found in S = 1 chains. First, we give a numerical approach of how to directly extract the projective representations from a matrixproduct state representation. Second, we derive nonlocal order parameters for inversion, and time reversal symmetry and discuss a generalized stringorder for internal symmetries. We furthermore point out that nonlocal order parameters for these \\\"topological phases\\\" are actually related to topological surfaces. 
Slides  
May 30, 2012  11:30  Imke Schneider  Lowenergy local density of states of the 1D Hubbard chain  Seminar 
Abstract
Lowenergy local density of states of the 1D Hubbard chain We examine the local density of states (DOS) at low energies numerically and analytically for the Hubbard model in one dimension. The eigenstates represent separate spin and charge excitations, which have a local DOS with a remarkably rich structure in space and energy. Our results predict signatures of strong correlations in the tunneling probability along finite quantum wires in scanning tunneling spectroscopy experiments.However, the detailed signatures can only be partly explained by standard Luttinger liquid theory. We discuss effects from higher order operators and boundary effects. 
Slides  
May 30, 2012  16:30  Michael Kastner  Equilibration times in closed longrange quantum spin models  Seminar 
Abstract
Equilibration times in closed longrange quantum spin models The approach to equilibrium is studied for longrange quantum Ising models where the interaction strength decays like r^{\\\\alpha} at large distances r. For a large class of observables and initial states, the expectation values are found to show a Gaussian decay in time. In a certain regime of the exponent \\\\alpha the corresponding relaxation time exhibits a nontrivial system size dependence. For the case where \\\\alpha does not exceed the lattice dimension, we prove analytically that, at a given instant of time t and for sufficiently large system size N, the expectation value of some observable (t) will practically be unchanged from its initial value (0). This finding implies that, for large enough N, equilibration effectively occurs on a time scale beyond any experimentally accessible one and will not be observed in practice. An experimental realization of such longrange interacting Ising models by means of trapped ions is also discussed. 
Slides  
May 31, 2012  11:30  Kirill Shtengel  From Majorana to parafermion quantum wires  Seminar  
May 31, 2012  16:30  Fabio Franchini  Approaching critical points through entanglement: why take one, when you can take them all?  Seminar 
Abstract
Approaching critical points through entanglement: why take one, when you can take them all? We report on our results on the entanglement entropy in 1dimensional, integrable, gaped systems. It is known that, for large system sizes, the Renyi entropy approaches a constant and in the scaling limit such constant is a function of the correlation length. For integrable models, this function can be written formally in terms of the partition function of a Conformal Field Theory, allowing to relate its asymptotic behavior to the operators in the theory. Using the Restricted SolidOnSolid models, we can consider a large class of minimal and parafermionic models, perturbed by different relevant operators and calculate the entanglement entropy for all of them. From the 8vertex model, we can access the entanglement of the XYZ spin1/2 chain. While for the RSOS we can provide a convincing interpretation of the corrections in terms of the operator content of the theory, the Renyi entropy of the XYZ chan seems to always be that of free fermions. 
Slides 