In this review recent investigations are summarized of many-body quantum systems with
long-range interactions, which are currently realized in Rydberg atom arrays, dipolar …

Spectral statistics of disordered systems encode Thouless and Heisenberg timescales,
whose ratio determines whether the system is chaotic or localized. We show that the scaling …

The efficient numerical simulation of nonequilibrium real-time evolution in isolated quantum
matter constitutes a key challenge for current computational methods. This holds in …

Quantum emulators, owing to their large degree of tunability and control, allow the
observation of fine aspects of closed quantum many-body systems, as either the regime …

Polynomially filtered exact diagonalization method (POLFED) for large sparse matrices is
introduced. The algorithm finds an optimal basis of a subspace spanned by eigenvectors …

We study the tV disordered spinless fermionic chain in the strong-coupling regime, t/V→ 0.
Strong interactions highly hinder the dynamics of the model, fragmenting its Hilbert space …

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 …

Recent work has focused on exploring many-body localization (MBL) in systems without
quenched disorder: one such proposal is Stark MBL in which small perturbations to a strong …

Despite enormous efforts devoted to the study of the many-body localization (MBL)
phenomenon, the nature of the high-energy behavior of the Heisenberg spin chain in a …

Studies of disordered spin chains have recently experienced a renewed interest, inspired by
the question to which extent the exact numerical calculations comply with the existence of a …