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 entanglement entropy of subsystems of typical eigenstates of quantum many-body
Hamiltonians has recently been conjectured to be a diagnostic of quantum chaos and …

This review summarizes recent advances in our understanding of anomalous transport in
spin chains, viewed through the lens of integrability. Numerical advances, based on tensor …

A bstract We study Krylov complexity in various models of quantum field theory: free massive
bosons and fermions on flat space and on spheres, holographic models, and lattice models …

We study disorder-induced ergodicity breaking transition in high-energy eigenstates of
interacting spin-1/2 chains. Using exact diagonalization, we introduce a cost function …

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 …

The concept of geometrical frustration has led to rich insights into condensed matter physics,
especially as a mechanism to produce exotic low-energy states of matter. Here we show that …

Certain disorder-free Hamiltonians can be nonergodic due to a strong fragmentation of the
Hilbert space into disconnected sectors. Here, we characterize such systems by introducing …

Eigenstate thermalization is widely accepted as the mechanism behind thermalization in
generic isolated quantum systems. Using the example of a single magnetic defect …

Integrable quantum systems of finite size are generically robust against weak enough
integrability-breaking perturbations, but become quantum chaotic and thermalizing if the …