Real space RG for dynamics of random spin chains and many-body 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 spin-1/2 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 many-body 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 many-body localization transition.

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 strong-correlation 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 non-trivial Z_2 invariant in 2D and 3D.

Exact corner free energies for two-dimensional integrable lattice models

We obtain long series expansions for the bulk, surface and corner free energies for several two-dimensional statistical models. The models encompass all integrable curves of the Q-state 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 fully-packed 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.

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 two-dimensional 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.

Fractional topological insulators

Topological band insulators are phases of matter with gapless edge modes that are protected by time-reversal 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.

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 Moore-Read. In this talk, we shall unify these two applications in the framework of spin systems. In this realm we shall discuss the Haldane-Shastry model in 1D and the Kalmeyer-Laughlin model in 2D, providing several generalizations of them.

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 so-called \"Moore-Read 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.

This is joint work with N. Read and E. Rezayi.

The computational power of AKLT states

In this talk I pursue a perhaps somewhat unfamiliar question: What is the computational power of quantum states?

A simple way of giving meaning to this question is through the scheme of measurement-based quantum computation [1]. Therein, the process of quantum computation is driven by *local* measurements on a highly entangled initial quantum state. Information is written onto that state, processed and read out by the measurements alone. Since the measurements are local, they can only destroy entanglement as they are applied. All entanglement needed in the computation must therefore provided by the initial state.

The initial state thus becomes a resource on which the power of the computational scheme depends. For the strongest resource states, measurement-based quantum computation becomes universal, i.e., everything that can possibly be computed by a quantum computer can be computed in this fashion. Examples for universal resources states are known [1], and they are also known to be rare [2].

It turns out that a quantum state with a long track record in condensed matter physics, the AKLT state on a honeycomb lattice, is a universal resource state for measurement-based quantum computation [3,4]. This is the main result I would like to present in this talk, after a general introduction to measurement-based quantum computation. I conclude with an extension of the above result, in which the AKLT Hamiltonian is continuously deformed. Numerical data suggests that the ground state of the deformed Hamiltonian undergoes a phase transition in computational power from universal to non-universal precisely at the point where disorder changes into Neel order [5].

* Joint work ([3]) with Tzu-Chieh Wei (Stony Brook) and Ian Affleck (UBC). A similar result has been obtained independently by A. Miyake (Perimeter Institute) [4]

* Relates to: Entanglement in extended systems, Tensor network states, [+1 slide about topological pha

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.
The holographic entanglement entropy for two disjoint intervals in the boundary theory is discussed, in particular for the time dependent backgrounds given by the Vaidya metrics, which model the black hole formation.

Non-Abelian spin textures

We present the following results for spin-full excitations over the Moore-Read quantum Hall state.
(i) The spin texture associated with an elementary charge e/4 excitation is identified with the polar core vortex that is known from the spin-1 BEC literature.
(ii) Upon fusing elementary charged spin textures, there is a locking between the resulting composite spin texture and the fusion sector of the underlying non-Abelian excitations over the Moore-Read state.

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.
Specifically we will discuss about
i) the choice of the Hilbert space and the specific LGTs suitable to simulations on optical lattices,
ii) how to prepare and address interesting states, such as ground states or low energy states of gauge invariant Hamiltonians,
iii) how to perform time evolution on such states.

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 non-equilibrium 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 large-time energy-transfer cumulants). This is based on works with Denis Bernard.

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.

Geometric phase contribution to quantum non-equilibrium many-body dynamics

In this talk I will study the influence of the geometry of a quantum systems underlying space of states on its quantum many-body dynamics. I will show that there is an interplay between dynamical and topological ingredients of quantum non-equilibrium 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, non-adiabatic 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 non-equilibrium phase transition between these two regimes.

Classical and quantum critical behaviors in trapped particle systems

Recent experiments on the Bose-Einstein 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.

The quantum and classical critical behaviors in nonhomogeneous trapped particle systems are discussed in the framework of the trap-size scaling theory, which extends the scaling Ansatz of the finite-size scaling theory of homogeneous systems.

Wave-functions and dualities in the "non-Abelian" sector of the Calogero-Sutherland model

The Calogero-Sutherland model is a 1D quantum model describing long range interacting particles. The (classical and) quantum Calogero-Sutherland 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.

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 set-up, we aim at simulating two-dimensional strongly-correlated layered fermions. These systems show remarkable physical properties due to the combination of statistics, interactions and dimensionality. Paradigmatic examples are high-Tc 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 Fermi-Hubbard Hamiltonians by superimposing optical lat- tices on the layers. These models are expected to unveil the physics of high-Tc superconductors. In particular, we want to simulate the attractive Fermi-Hubbard model whose rich phenomenology should be more accessible in the experiment [5].

[1] R. Feynman, International Journal of Theoretical Physics,Vol. 21, (1982).
[2] I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008); M. Lewenstein, et al., Adv. Phys. 56, 243-379 (2007); T. Esslinger, Condensed Matter Physics 1 (2010).
[3] L. Fallani, C. Fort, M. Inguscio Adv. At. Mol. Opt. Phys. 56, 119-160 (Academic Press, 2008). [4] Y. Dubi, et al. Nature, 449:876880, (2007).
[5] A. Ho, M. Cazalilla, and T. Giamarchi, Phy

Entanglement spectrum in quantum many body systems

The entanglement between two parts of a many-body system can be characterized in detail by the entanglement spectrum. Focusing on gapped phases of one-dimensional systems, I will show how this spectrum is dominated by contributions from the boundary between the parts. The boundary-local nature of the entanglement spectrum is clarified through its hierarchical level structure, through the combination of two single-boundary spectra to form a two-boundary 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.

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 non-abelian potential. We consider a 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 the presence of strong repulsive interactions, deformed Laughlin ground states occur in general. However, at the degeneracy points of the Landau levels, non-abelian quantum Hall states may appear. In the second part I will discuss anisotropic Ginzburg-Landau and Lawrence-Doniach models describing a layered superfluid ultracold Fermi gas in optical lattices. We derive the coefficients of the anisotropic Ginzburg-Landau 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 Lawrence-Doniach model - often used to describe the 2D-3D dimensional crossover in layered superconductors - for a layered ultracold Fermi gas, obtaining a relation between the interlayer Josephson couplings and the Ginzburg-Landau masses. A discussion of effective models for the dynamics of Fermi gases in layered optical lattices is as well presented.

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.

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 many-body localization transition conjecture.

Investigating the momentum distribution of 1D quasi-condensates

The dynamical structure factor S(q,ω) provides an important depiction of the dynamic behavior of quantum many-body systems. For gaseous Bose-Einstein 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 light-scattering (Bragg spectroscopy), that couples two momentum states of the same internal ground-state by a stimulated two-photons transition. In this work, we have characterized one-dimensional chains of bosons in the quasi-condensate regime, realized by loading a Bose-Einstein condensate of Rb-87 in a pair of orthogonal red-detuned 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 time-of-flight absorption imaging can be used as alternative simple probe to directly measure the coherence length of one-dimensional 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. Clément, L. Fallani, C. Fort, and M. Inguscio, Physical Review A 83, 031604(R) (2011).

Two-electron Quantum Gases in Florence

We will present the LENS experimental activity on quantum degenerate two-electron atoms. We will report on the recent production of ytterbium Bose-Einstein condensates and illustrate the possibilities that are offered by this system for quantum simulation and quantum information experiments.

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.

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].

[1] R. Egger, A. Zazunov, and A. Levy Yeyati: Phys. Rev. Lett. 105, 136403 (2011)
[2] A. Zazunov, A.Levy Yeyati, and R. Egger: Phys. Rev B 84, 165440 (2011)

Dynamics of impurities in a one-dimensional Bose gas

In a recent experiment [1], we have used a largely imbalanced mixture of K41 and Rb87 to create impurities in a one-dimensional gas of bosons. The impurity K41 atoms, initially localized by means of a species-selective optical potential, were abruptly released and let expand and oscillate in the one-dimensional 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 clear-cut 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 mass-shift model formulated following Feynman variational method [2].

[1] J. Catani et al., Phys. Rev. A 85, 023623 (2012)
[2] R. P. Feynman, Phys. Rev. 97, 660 (1955)

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 non-interacting 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.

Dynamic correlations, fluctuation-dissipation relations and effective temperatures after a quantum quench of the Ising chain

Fluctuation-dissipation relations and effective temperatures have been successfully used to describe the non-equilibrium behavior of classical system and quantum glasses in contact with thermal baths. We extend this approach to quantum isolated many-body 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.

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 matrix-product state representation. Second, we derive non-local order parameters for inversion, and time reversal symmetry and discuss a generalized string-order for internal symmetries. We furthermore point out that non-local order parameters for these \\\"topological phases\\\" are actually related to topological surfaces.

Low-energy 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.

Equilibration times in closed long-range quantum spin models

The approach to equilibrium is studied for long-range 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 non-trivial 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 long-range interacting Ising models by means of trapped ions is also discussed.

Approaching critical points through entanglement: why take one, when you can take them all?

We report on our results on the entanglement entropy in 1-dimensional, 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 Solid-On-Solid 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 8-vertex model, we can access the entanglement of the XYZ spin-1/2 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.