Over the last decade impressive progress has been made in the theoretical understanding
of transport properties of clean, one-dimensional quantum lattice systems. Many physically …

The many-body physics at quantum phase transitions shows a subtle interplay between
quantum and thermal fluctuations, emerging in the low-temperature limit. In this review, we …

A bstract We apply a notion of quantum complexity, called “Krylov complexity”, to study the
evolution of systems from integrability to chaos. For this purpose we investigate the …

The dynamical convergence of a system to the thermal distribution, or Gibbs state, is a
standard assumption across all of the physical sciences. The Gibbs state is determined just …

In the past decades, it was recognized that quantum chaos, which is essential for the
emergence of statistical mechanics and thermodynamics, manifests itself in the effective …

Unitary designs have become a vital tool for investigating pseudorandomness, since they
approximate the statistics of the uniform Haar ensemble. Despite their central role in …

The eigenstate thermalization hypothesis explains the emergence of the thermodynamic
equilibrium in isolated quantum many-body systems by assuming a particular structure of …

Using numerical exact diagonalization, we study matrix elements of a local spin operator in
the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the …

We investigate many-body dynamics where the evolution is governed by unitary circuits
through the lens of “Krylov complexity,” a recently proposed measure of complexity and …

Atypical eigenstates in the form of quantum scars and fragmentation of Hilbert space due to
conservation laws provide obstructions to thermalization in the absence of disorder. In …