Measurement-induced phase transitions (MIPT) were discovered for chaotic random quantum model undergoing projective or continuous measurements. In these models, depending on the rate of measurement, the system is either in an entangling phase or disentangling phase. The existence of MIPT was first demonstrated for quantum systems using quantities such as entanglement or Rényi entropy for the characterization of the phase transition. In this talk, I will present a classical model showing the same phenomenology which consists of a single random…

Assuming only a known dispersion relation of a single mode in the spectrum of a two-point function in some quantum field theory, we investigate when and how the reconstruction of the complete spectrum of physical excitations is possible. In particular, we develop a constructive algorithm based on the theorems of Darboux and Puiseux that allows for such a reconstruction of all modes connected by level-crossings. For concreteness, we focus on theories in which the known mode is a gapless excitation…

Recently introduced dual unitary brickwork circuits have been recognised as paradigmatic exactly solvable quantum chaotic many-body systems with tunable degree of ergodicity and mixing. In this talk we show that regularity of the circuit lattice is not crucial for exact solvability. We consider a circuit where random 2-qubit dual unitary gates sit at intersections of random arrangements of straight lines in two dimensions (mikado) and analytically compute the variance of the spatio-temporal correlation function of local operators. Note that the…

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…