Rényi entropies are conceptually valuable and experimentally relevant generalisations of the celebrated von Neumann entanglement entropy. After a quantum quench in a clean quantum many-body system they generically display a universal linear growth in time followed by saturation. While a finite subsystem is essentially at local equilibrium when the entanglement saturates, it is genuinely out-of-equilibrium in the growth phase. In particular, the slope of the growth carries vital information on the nature of the system's dynamics, and its characterisation is a key objective of current research. In the…

The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor in coupled bipartite chaotic quantum systems and obtain all moments of the spectral form factor exactly in the semiclassical limit of large Hilbert space dimension. Extrapolating those results to finite Hilbert space dimension we find a universal dependence of the spectral form factor on a single scaling parameter for times larger…

Universality asserts that, especially near phase transitions, the macroscopic properties of a physical system do not depend on its details such as the precise form of microscopic interactions. We show that the two best-known examples of dynamical universality classes, the diffusive and Kardar-Parisi-Zhang-classes, are only part of an infinite discrete family. The members of this family have dynamical exponents which surprisingly can be expressed by the Kepler ratio of consecutive Fibonacci numbers. This strongly indicates the existence of a simpler…

We apply the non-Abelian time evolving block decimation (TEBD) approach to study out of equilibrium properties of interacting many-body systems. We first show how we can use this approach to capture dynamical composite particle formation in SU(3) Hubbard models, where a large class of initial states is shown to develop into a negative temperature gas of strongly interacting ‘hadrons'. Then we extend non-Abelian TEBD to open systems with Lindbladian time evolution. As an illustration, we study the one-dimensional SU(2) Hubbard…

In this talk, we investigate the behavior of purity and out-of-time-ordered correlations in random quantum circuits. We show that the time evolution of both quantities can be described by a Markov chain, and their relaxation towards their asymptotic values is not governed by the second largest eigenvalue of the transfer matrix, as one could expect. The exponential relaxation is instead given by an ``eigenvalue'', which is not in the spectrum of the transfer matrix at all -- a phantom eigenvalue.…

The study of quantum quenches had a vast contribution to our understanding of out-of-equilibrium dynamics and relaxation in closed many-body systems. The investigation of entanglement growth in a quench could shed light to various features of the underlying physics, in particular for integrable systems. However, most of the studies focus on setups where the system is driven far from equilibrium due to the inhomogeneity of the initial state. In my talk, I will present results for quenches where the time evolution operator is made…