I will discuss a general procedure to construct an integrable real--time trotterization of interacting lattice models. As an illustrative example we will consider a spin-$1/2$ chain, with continuous time dynamics described by the isotropic ($XXX$) Heisenberg Hamiltonian. I will derive local conservation laws from an inhomogeneous transfer matrix and construct a boost operator. In the continuous time limit these local charges reduce to the known integrals of motion of the Heisenberg chain. In a simple Kraus representation I will examine the nonequilibrium setting, where…

In this talk I will argue that novel ordered phases can be expected for interacting quantum systems away from thermal equilibrium. I will start by reporting a set of mean-field results concerning the effects of large bias voltages applied across an half-filled Hubbard chain. As a function of the applied voltage and temperature a rich set of phases can be found that is induced by the interplay between electron-electron interactions and non-equilibrium conditions. Taking a step back, I try to…

I'll give a short review of the recent theoretical progress to explicitly construct non-thermal steady states in quantum systems such as interacting bosons and spin chains. Moreover, I'll present the recently introduced hydrodynamic description of such non-thermal steady states that allows to study (ballistic) transport properties of many-body systems and to construct non-equilibrium steady states with persistent energy or spin currents and stronger quantum correlations. * Jacopo De Nardis, École normale supérieure de Paris

In this talk, we shall consider the classical field theory of the Heisenberg ferromagnet, which is the semi-classical limit of the Heisenberg spin-1/2 chain. Our primary motivation to study classical solvable dynamical system is to understand the similarities and differences between integrable quantum systems and their classical counterparts. Unfortunately, there seem to exist no efficient computational framework to achieve this goal. To this end, by starting from first principles and employing the finite-gap algebro-geometric integration technique, we identify a certain…

It is a well known fact that the spreading of information in lattice quantum systems is not instantaneous, but it rather exists a maximum velocity dictated by the Lieb-Robinson bound.The existence of such a lightcone deeply affects equilibrium properties as well as out-of-equilibrium ones, which have been a subject of outstanding interest in the recent years.In this talk, a novel out-of-equilibrium protocol critically affected by the presence of a maximum velocity is proposed and discussed. Specifically, a one dimensional lattice…

In the limit of small ħ, e.g. short wavelengths, semi-classical theory provides a connection between the spectrum of a quantum mechanical system and the periodic orbits of its classical counter part. While this is well established for systems with few degrees of freedom the extension to many-body systems is challenging as the system dimension N  turns into an additional large parameter. For a long chain of interacting kicked tops short time spectral information may be obtained using a duality relation between…

My talk will present two recently uncovered connections between hydrodynamics and many-body chaos—one at strong and one at weak coupling. I will begin by introducing some relevant concepts from the field of relativistic hydrodynamics, which will be followed by a short discussion of holographic duality. In particular, I will describe how thermal field theory correlation functions can be inferred from the properties of black holes. I will then show how in strongly interacting theories with simple holographic duals both the…

It is well known that typical pure states in the Hilbert space are (nearly) maximally entangled. In my talk I will discuss, from the perspective of bipartite entanglement entropy, how different are typical eigenstates of physical Hamiltonians from typical states in the Hilbert space. In the first part, I will present tools to compute the average entanglement entropy of all eigenstates of translationally-invariant quadratic fermionic Hamiltonians, and derive exact bounds . I will prove that (i) if the subsystem volume…