Statistical mechanics provides a framework for describing the physics of large, complex
many-body systems using only a few macroscopic parameters to determine the state of the …

We study time dynamics of 1D disordered Heisenberg spin-1/2 chains focusing on a regime
of large system sizes and a long-time evolution. This regime is relevant for observation of …

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 …

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 …

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 review the application of level dynamics to spectra of quantally chaotic systems. We
show that the statistical mechanics approach gives us predictions about level statistics …

We perform a thorough and complete analysis of the Anderson localization transition on
several models of random graphs with regular and random connectivity. The unprecedented …

Quantum many-body scars (QMBS) constitute a new quantum dynamical regime in which
rare “scarred” eigenstates mediate weak ergodicity breaking. One open question is to …

We study many-body localization (MBL) transition in disordered Floquet systems using a
polynomially filtered exact diagonalization (POLFED) algorithm. We focus on disordered …

We compare the accuracy of two prime time evolution algorithms involving matrix product
states—tDMRG (time-dependent density matrix renormalization group) and TDVP (time …