Many-body localization in the age of classical computing

P Sierant, M Lewenstein, A Scardicchio… - Reports on Progress …, 2024 - iopscience.iop.org
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 …

[HTML][HTML] Many-body localization: An introduction and selected topics

F Alet, N Laflorencie - Comptes Rendus Physique, 2018 - Elsevier
What happens in an isolated quantum system when both disorder and interactions are
present? Over the recent years, the picture of a non-thermalizing phase of matter, the many …

Distinguishing localization from chaos: Challenges in finite-size systems

DA Abanin, JH Bardarson, G De Tomasi… - Annals of Physics, 2021 - Elsevier
We re-examine attempts to study the many-body localization transition using measures that
are physically natural on the ergodic/quantum chaotic regime of the phase diagram. Using …

Introduction to random matrices theory and practice

G Livan, M Novaes, P Vivo - Monograph Award, 2018 - ems.press
In their preface, the authors state that 'this is a book for absolute beginners'. Well, that
depends on the definition of a beginner! Here,(s) he should be thoroughly at home in …

[HTML][HTML] Integrals of motion in the many-body localized phase

V Ros, M Müller, A Scardicchio - Nuclear Physics B, 2015 - Elsevier
We construct a complete set of quasi-local integrals of motion for the many-body localized
phase of interacting fermions in a disordered potential. The integrals of motion can be …

Colloquium: Many-body localization, thermalization, and entanglement

DA Abanin, E Altman, I Bloch, M Serbyn - Reviews of Modern Physics, 2019 - APS
Thermalizing quantum systems are conventionally described by statistical mechanics at
equilibrium. However, not all systems fall into this category, with many-body localization …

Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states

DM Basko, IL Aleiner, BL Altshuler - Annals of physics, 2006 - Elsevier
We consider low-temperature behavior of weakly interacting electrons in disordered
conductors in the regime when all single-particle eigenstates are localized by the quenched …

Anderson transitions

F Evers, AD Mirlin - Reviews of Modern Physics, 2008 - APS
The physics of Anderson transitions between localized and metallic phases in disordered
systems is reviewed. The term “Anderson transition” is understood in a broad sense …

Local integrals of motion in many‐body localized systems

JZ Imbrie, V Ros, A Scardicchio - Annalen der Physik, 2017 - Wiley Online Library
We review the current (as of Fall 2016) status of the studies on the emergent integrability in
many‐body localized models. We start by explaining how the phenomenology of fully many …

Electrons in disordered systems and the theory of localization

DJ Thouless - Physics Reports, 1974 - Elsevier
This paper gives a review of the theory of noninteracting electrons in a static disordered
lattice. The introductory section gives a brief survey of the main aspects of the problem and …