Many-body localization: stability and instability

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
Wojciech De Roeck, John Z Imbrie

Abstract

Rare regions with weak disorder (Griffiths regions) have the potential to spoil localization. We describe a non-perturbative construction of local integrals of motion (LIOMs) for a weakly interacting spin chain in one dimension, under a physically reasonable assumption on the statistics of eigenvalues. We discuss ideas about the situation in higher dimensions, where one can no longer ensure that interactions involving the Griffiths regions are much smaller than the typical energy-level spacing for such regions. We argue that ergodicity is restored in dimension d>1, although equilibration should be extremely slow, similar to the dynamics of glasses.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

References

Feb 15, 1991·Physical Review. a·J M Deutsch
Aug 1, 1994·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·M Srednicki
Apr 19, 2008·Nature·Marcos RigolMaxim Olshanii
Apr 27, 2011·Physical Review Letters·Michael Aizenman, Simone Warzel
Oct 8, 2013·Physical Review Letters·Maksym SerbynDmitry A Abanin
Mar 15, 2015·Physical Review Letters·S S KondovB DeMarco
Nov 14, 2015·Physical Review Letters·Trithep Devakul, Rajiv R P Singh
Jun 25, 2016·Science·Jae-yoon ChoiChristian Gross
Jul 26, 2016·Physical Review Letters·John Z Imbrie
Oct 22, 2016·Physical Review Letters·B L AltshulerV E Kravtsov
Dec 24, 2016·Physical Review Letters·N Y YaoJ E Moore
Oct 28, 2017·Physical Review Letters·David J LuitzWojciech De Roeck

❮ Previous
Next ❯

Citations

Nov 1, 2017·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Michael PepperSteven Simon
Jul 17, 2019·Nature Materials·Yaroslav A GerasimenkoDragan Mihailovic
Mar 12, 2020·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Amos Chan, Thorsten B Wahl
Apr 26, 2019·Proceedings of the National Academy of Sciences of the United States of America·Evert van NieuwenburgGil Refael
Oct 24, 2020·Physical Review Letters·Elmer V H DoggenDmitry G Polyakov
May 22, 2021·Physical Review Letters·Eli ChertkovBryan K Clark

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
Michael PepperSteven Simon
Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
Trithep DevakulS L Sondhi
© 2022 Meta ULC. All rights reserved