Related papers: Level statistics across the many--body localizatio…
We study the energy level spacing of perturbed conformal minimal models in finite volume, considering perturbations of such models that are massive but not necessarily integrable. We compute their spectrum using a renormalization group…
In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…
This paper considers a novel problem, bi-level graphical modeling, in which multiple individual graphical models can be considered as variants of a common group-level graphical model and inference of both the group- and individual-level…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
Randomness and disorder have strong impact on transport processes in quantum systems and give rise to phenomena such as Anderson localization [1-3], many-body localization [4] or glassy dynamics [5]. Their characteristics thereby depend on…
Level statistics is discussed for XXZ spin chains with discrete symmetries for some values of the next-nearest-neighbor (NNN) coupling parameter. We show how the level statistics of the finite-size systems depends on the NNN coupling and…
We review recent advances in understanding the universal scaling properties of non-equilibrium phase transitions in non-ergodic disordered systems. We discuss dynamical critical points (also known as eigenstate phase transitions) between…
We study the universal properties of eigenstate entanglement entropy across the transition between many-body localized (MBL) and thermal phases. We develop an improved real space renormalization group approach that enables numerical…
Theoretical expressions for the distribution of the ratio of consecutive level spacings for quantum systems with transiting dynamics remain unknown. We propose a family of one-parameter distributions $P(r)\equiv P(r;\beta)$, where…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
We study spectral statistics in systems with a mixed phase space, in which regions of regular and chaotic motion coexist. Increasing their density of states, we observe a transition of the level-spacing distribution P(s) from Berry-Robnik…
Experimental progress in atomic, molecular, and optical platforms in the last decade has stimulated strong and broad interest in the quantum coherent dynamics of many long-range interacting particles. The prominent collective character of…
We study the many-body localization aspects of single-particle mobility edges in fermionic systems. We investigate incommensurate lattices and random disorder Anderson models. Many-body localization and quantum nonergodic properties are…
We present a finite-size scaling for both interaction and disorder strengths in the critical regime of the many-body localization (MBL) transition for a spin-1/2 XXZ spin chain with a random field by studying level statistics. We show how…
This paper studies multivariate nonparametric change point localization and inference problems. The data consists of a multivariate time series with potentially short range dependence. The distribution of this data is assumed to be…
We study the statistical properties of energy spectra of two-dimensional quasiperiodic tight-binding models. We demonstrate that the nearest-neighbor level spacing distributions of these non-random systems are well described by random…
We study the influence of a correlated disorder on the localization phase transition in the pinning model. When correlations are strong enough, a strong disorder regime arises: large and frequent attractive regions appear in the…
We study a quantum spin system with local bilinear interactions and without quenched disorder which seems to display characteristic signatures of a many-body localisation (MBL) transition. From direct diagonalisation of small systems, we…
We study the potential influence of the particle multi-occupations on the stability of many-body localization in the disordered Bose-Hubbard model. Within the higher-energy section of the dynamical phase diagram, we find that there is no…
The level curvature distribution function is studied both analytically and numerically for the case of T-breaking perturbations over the orthogonal ensemble. The leading correction to the shape of the curvature distribution beyond the…