Exactly solved models of many-body quantum chaos

Abstract
I will discuss the problem of unreasonable effectiveness of random matrix theory for description of spectral fluctuations in extended quantum lattice systems. A class of locally interacting spin systems has been recently identified where the spectral form factor is proven to match with gaussian or circular ensembles of random matrix theory, and where spatiotemporal correlation functions of local observables as well as some measures of dynamical complexity can be calculated analytically. These, so-called dual unitary systems, include integrable, non-ergodic, ergodic, and generically, (maximally) chaotic cases. After reviewing the basic results on dual unitary Floquet circuits, I will argue that correlation functions of these models are generally perturbatively stable with respect to breaking dual-unitarity, and describe a simple result within this framework.
BIO
T. Prosen has received a PhD in theoretical physics in 1995 from University of Ljubljana. After a postdoctoral stay at Institut Henri Poincare in Paris he obtained a permanent position at University of Ljubljana in 1996, first as a researcher, since 1999 as an assistant professor, and since 2008 as a full professor. He is a head of research group on Nonequilibrium quantum and statistical physics at the Faculty of mathematics and physics in Ljubljana, and recipient of the Advanced grant of European research council in 2016. Prosen's main research interests are related to dynamics of interacting systems, both related to Hamiltonian or quantum chaos, and integrability. Among other things, he has developed methods for solving many-body Lindblad equations, in particular in the presence of boundary driving and integrable interactions, which lead to a discovery of quasi-local charges and rigorous lower bounds on previously controversial high temperature ballistic spin transport in XXZ chains.