I will introduce and study a class of models of free fermions hopping between neighbouring sites with random Brownian amplitudes. These simple models describe stochastic, diffusive, quantum, unitary dynamics. I focus on periodic boundary conditions and derive the complete stationary distribution of the system. It is proven that the generating function of the latter is provided by the Harish-Chandra-Itzykson-Zuber integral which allows us to access all fluctuations of the system state. The steady state is characterized by non trivial correlations which have a topological nature. In the thermodynamic large system size limit, the system approaches a non random equilibrium state plus occupancy and coherence fluctuations of magnitude scaling proportionally with the inverse of the square root of the volume. The large deviation function for those fluctuations is determined. Although decoherence is effective on the mean steady state, we observe that sub-leading fluctuating coherences are dynamically produced from the inhomogeneities of the initial occupancy profile.

***** *Tony Jin, LPT ENS Paris*

Out-of-equilibrium systems have nowadays an important role in 1d statistical physics. Although an equilibrium state obviously doesn’t exist for such systems, one looks for a steady state (that is stationary in time). It is defined as the zero-eigenvalue eigenstate of the Markov matrix that describe the evolution of the system. Its exact computation is at the core of many researches.

In some cases, the matrix product state ansatz (matrix ansatz for short) allows to compute this steady state. However no general approach for this ansatz is known. On the other hand, many 1d statistical models appear to be integrable, which allows to get eigenstates of the Markov matrix through Bethe ansatz. The goal of this presentation is to show how integrability gives a natural framework to construct the matrix ansatz for 1d systems with boundaries.

It can be done on very general grounds, allowing to construct the matrix ansatz when it is not known, and also to define new models and/or to find boundary conditions ‘adapted’ to the model under consideration. We will illustrate the technique on some examples.

*** ***Eric Ragoucy, Laboratoire d’Annecy-le-Vieux de Physique Théorique, Annecy, France*

**FMF, University of Ljubljana, 14th to 17th November 2018**

Speakers: Fabian Heidrich-Meisner, Herbert Spohn, Peter Prelovšek, Maurizio Fagotti, Joel Moore, Bruno Bertini, Lenart Zadnik, Katja Klobas, Marko Ljubotina and Gyorgy Feher. The schedule can be found here.

*The event will take place at the Kuščer Seminar room, 4*^{th}* floor, Jadranska 19, except for the Wednesday afternoon session, which takes place in the room 3.07, 3*^{rd}* floor, Jadranska 21.*

We consider a Lindblad time evolution of an open quantum system with dissipation acting on a subset of the degrees of freedom *H*_{0}, and targeting a unique dark state in *H*_{0}. It is argued, that in the Zeno limit of strong dissipation, the density matrix of the system traced over the dissipative subspace *H*_{0}, evolves according to another Lindblad dynamics, with an effective Hamiltonian and weak effective dissipation. This, in turn, allows to calculate the steady state in Zeno limit via a diagonalization of the effective Hamiltonian.

*** ***Vladislav Popkov, Universität Bonn*

[1] Link to the preprint.

I will present work in progress with Marko Ljubotina. We will discuss quasilocal conservation laws in the Trotterized XXZ model and their implications on the spin transport. Interestingly, the model exhibits ballistic transport even for a range of anisotropies which pertain to the gapped regime in the continuous-time limit.

*** ***Lenart Zadnik, Faculty of Mathematics and Physics, University of Ljubljana*

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*