We review selected advances in the theoretical understanding of complex quantum many-
body systems with regard to emergent notions of quantum statistical mechanics. We cover …

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

In the ongoing discussion on thermalization in closed quantum many-body systems, the
eigenstate thermalization hypothesis has recently been proposed as a universal concept …

We explore the relation between the entanglement of a pure state and its energy variance
for a local one-dimensional Hamiltonian, as the system size increases. In particular, we …

We propose a way to construct a thermal pure quantum matrix product state (TPQ-MPS) that
can simulate finite-temperature quantum many-body systems with a minimal numerical cost …

For quantum many-body systems in one dimension, computational complexity theory
reveals that the evaluation of ground-state energy remains elusive on quantum computers …

The question of how systems respond to perturbations is ubiquitous in physics. Predicting
this response for large classes of systems becomes particularly challenging if many degrees …

We develop a formula to evaluate the purity of a series of thermal equilibrium states that can
be calculated in numerical experiments without knowing the exact form of the quantum state …

We investigate how the observable relaxation behavior of an isolated quantum many-body
system is modified in response to weak-to-moderate perturbations within a nonperturbative …

We study the real-time dynamics of local occupation numbers in a one-dimensional model of
spinless fermions with a random on-site potential for a certain class of initial states. The latter …