We demonstrate the existence of a new quantum phase of matter that arises in antiferromagnetic spin chains with a weak frustration -just one bond in a large chain-. This is the case, for instance, in systems with an odd number of spins with periodic boundary conditions. Such new phase is extended, gapless, but non-relativistic: the low-energy excitations have a quadratic (Galilean) spectrum. Locally, the correlation functions in the ground state do not show significant deviations, compared to the non-frustrated case, but correlators involving a number of sites (or distances) scaling like the system size display new behaviors. In particular, the von Neumann entanglement entropy is found to follow new rules, for which neither area law applies, nor one has a divergence of the entropy with the system size. Such very long-range correlations are novel and of potential technological interest. We display such new phase in a few prototypical chains using numerical simulations and we study analytically the paradigmatic example of the Ising chain. Through these examples we argue that this phase emerges generally in (weakly) frustrated systems with discrete symmetries.

*** ***Fabio Franchini, Ruđer Bošković Institute, Zagreb*

[1] Salvatore Marco Giampaolo, Flávia Braga Ramos, Fabio Franchini, *arXiv:1807.07055*

In this talk, we will present a framework for the quantification of the capability of various quantum processes to generate coherence. The relevant measures, admitting computable expressions, are based on probabilistic averages and arise naturally from the viewpoint of coherence as a resource. We will focus mainly on *unitary evolutions *and various *dephasing processes, *including Lindblad dynamics that dephase in the long-time limit. The latter will turn out to have, in specific cases, optimal coherence-generating power for some intermediate time.

*** ***Georgios Styliaris, USC Dornsife, Department of Physics and Astronomy*

We study a one-dimensional system of quantum particles in a tight-binding model with infinite on-site repulsion. We introduce an efficient method to calculate one-body correlation functions of states with Néel ordering of spin flavors. For the ground state of this spin ordering, we observe a Gaussian decay of the correlation function. Upon increasing the temperature, the Gaussian decay gradually transforms into an exponential decay.

*** ***Yicheng Zhang, Department of Physics, Penn State*

Many-body quantum systems in one dimension have many remarkable characteristics as compared to their higher-dimensional counterparts. On the formal side, advanced nonperturbative methods such as integrability can be used to compute their physical properties, which are nowadays accessible in real experiments on magnetic systems and cold atoms. Moreover, their relaxation and equilibration behaviour cannot be simply described by traditional textbook methods, and can lead to long-lived non-thermal equilibrium states. This talk will provide an overview of current research in this area, and introduce recently-discovered methods to treat quenched and driven systems in various experimentally-relevant contexts.

*** ***Jean-Sébastien Caux, Institute of Physics, University of Amsterdam*

In recent years, the field of theoretical physics has experienced a revival of interest in the exploration of integrable and quantum chaotic properties of physical systems. This workshop aims to bring together researchers from condensed matter, mathematical and high-energy physics communities to facilitate a cross-disciplinary discussion on these rapidly evolving developments.

The workshop will be held between 3 – 9 June, 2018, in Bled, Slovenia.

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 [1]. I will prove that (i) if the subsystem volume is a finite fraction of the system volume, then the average entanglement entropy is smaller than the result for typical pure states in the thermodynamic limit (the difference is extensive with system volume), and (ii) in the limit in which the subsystem volume is a vanishing fraction of the system volume, the average entanglement entropy is maximal; i.e., typical eigenstates of such Hamiltonians exhibit eigenstate thermalization.

In the second part, I will focus on eigenstates of quantum chaotic many-body Hamiltonians [2]. I will prove that, in a system that is away from half filling and divided in two equal halves, an upper bound for the average entanglement entropy of random pure states with a fixed particle number and normally distributed real coefficients exhibits a deviation from the maximal value that grows with the square root of the volume of the system. Exact numerical results for highly excited eigenstates of a particle number conserving quantum chaotic model indicate that the bound is saturated with increasing system volume.

*** ***Lev Vidmar, F1 Department of Theoretical Physics, IJS*

[1] Vidmar, Hackl, Bianchi and Rigol, Phys. Rev. Lett. **119**, 020601 (2017)

[2] Vidmar and Rigol, Phys. Rev. Lett. **119**, 220603 (2017)

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 Lyapunov exponent and the butterfly velocity can be computed from a retarded longitudinal energy-energy two-point function, without the need for computing the OTOC. This makes the connection between holographic many-body chaos and hydrodynamics precise. Finally, by constructing a modified kinetic, Boltzmann-like equation, both phenomenologically and from an OTOC, I will argue that even at weak coupling, hydrodynamic and chaotic properties can be intimately related.

***** *Sašo Grozdanov, MIT – Center for Theoretical Physics*

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 the temporal and spatial evolution. This allows a direct comparison to the classical periodic orbits of the system. It reveals that this class of system possesses non-isolated orbit manifolds whose contributions to the trace formula are strongly dominant. For large *N* their presence leads to remarkably strong spectral fluctuations, which are not recovered by conventional semi-classical theory.

*** ***Maram Akila, **Universität Duisburg-Essen*

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 model is considered, where a localized impurity is suddenly created and then dragged at a constant velocity.

Focussing on a simple, but far from trivial, free model the response of the system at late times is analyzed, with emphasis on its transport properties. The finite maximum velocity is responsible for a rich phenomenology, for which exact results are provided. Taking into account the experience acquired so far, more general models are discussed and unpublished results presented, with exact predictions in completely generic (non integrable) one dimensional lattice systems.

*** ***Alvise Bastianello, SISSA Trieste*

[1] A. Bastianello, A. De Luca, *Phys. Rev. Lett.* **120**, 060602 (2018).

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 scaling procedure of the corresponding degenerate large-genus Riemann surfaces which provides a statistical description for a thermodynamic gas of magnetic solitons. Using simple arguments of semi-classical quantization, we use the classical S-matrix to derive a universal integral dressing equation for the spectral distribution function of soliton excitations which accounts for interactions with a non-trivial many-body vacuum. By lifting the conventional theory of Whitham modulations equations to the thermodynamic setting, we obtain a simple formula for the effective propagation velocity which is, remarkably, in formal agreement with that proposed recently for quantum integrable models.

*** ***Enej Ilievski, Universiteit van Amsterdam*