Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1607.05756 · Physical Review X

Critical Properties of the Many-Body Localization Transition

Vedika Khemani, S. P. Lim, D. N. Sheng, David A. Huse

Published Apr 25, 2017• 256 citations
arXivHTMLPDF

Abstract

Some quantum systems can enter a many-body localized (MBL) phase, where the particles do not settle into thermal equilibrium but remain stuck in some initial state. A new theoretical analysis explores the transition between MBL and thermal phases and finds that the transition is driven by the growth of a network of quantum entanglement.
DOI
10.1103/physrevx.7.021013

Related papers

Quantum Thermalization and Localization in a Trapped Ion Quantum Simulator

Jacob Smith

When a system thermalizes it loses all memory of its initial conditions. Even within a closed quantum system, subsystems usually thermalize using the rest of the system as a heat bath. Exceptions to quantum thermalization have been observed, but typically require inherent symmetries or noninteracting particles in the presence of static disorder. The prediction of many-body localization (MBL), in which disordered quantum systems can fail to thermalize despite strong interactions and high excitation energy, was therefore surprising and has attracted considerable theoretical attention. We experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmably random disorder to ten spins initialized far from equilibrium with respect to the Hamiltonian. Using experimental and numerical methods we observe the essential signatures of MBL: initial state memory retention, Poissonian distributed many-body energy level spacings, and evidence of long-time entanglement growth. Our platform can be scaled to more spins, where detailed modeling of MBL becomes impossible.

•Jan 1, 2016•0 citations

Rare‐region effects and dynamics near the many‐body localization transition

Kartiek Agarwal, Ehud Altman, Eugene Demler +3 more

The low‐frequency response of systems near the many‐body localization phase transition, on either side of the transition, is dominated by contributions from rare regions that are locally “in the other phase”, i.e., rare localized regions in a system that is typically thermal, or rare thermal regions in a system that is typically localized. Rare localized regions affect the properties of the thermal phase, especially in one dimension, by acting as bottlenecks for transport and the growth of entanglement, whereas rare thermal regions in the localized phase act as local “baths” and dominate the low‐frequency response of the MBL phase. We review recent progress in understanding these rare‐region effects, and discuss some of the open questions associated with them: in particular, whether and in what circumstances a single rare thermal region can destabilize the many‐body localized phase. image

arXiv:1611.00770•Annalen der Physik•Jan 12, 2017•211 citations

Characterizing the many-body localization transition using the entanglement spectrum

S D Geraedts, Nicolas Regnault, Rahul Nandkishore

We numerically explore the many body localization (MBL) transition through the lens of the entanglement spectrum . While a direct transition from localization to thermalization is believed to be obtained in the thermodynamic limit (the exact details of which remain an open problem), in finite system sizes there exists an intermediate 'quantum critical' regime. Previous numerical investigations have explored the crossover from thermalization to criticality, and have used this to place a numerical lower bound on the critical disorder strength for MBL. A careful analysis of the high energy part of the entanglement spectrum (which contains universal information about the critical point) allows us to study the crossover from criticality to MBL, and we find evidence for such a crossover which could allow us to place a numerical upper bound on the critical disorder strength for MBL.

arXiv:1705.00631•New Journal of Physics•Oct 16, 2017•47 citations

Eigenstate phase transitions and the emergence of universal dynamics in highly excited states

S. A. Parameswaran, Andrew C. Potter, Romain Vasseur

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 different many‐body localized (MBL) phases, and between MBL and thermal phases. image

arXiv:1610.03078•Annalen der Physik•Jan 20, 2017•60 citations

Many-Body Localization and Thermalization in Quantum Statistical Mechanics

Rahul Nandkishore, David A. Huse

We review some recent developments in the statistical mechanics of isolated quantum systems. We provide a brief introduction to quantum thermalization, paying particular attention to the eigenstate thermalization hypothesis (ETH) and the resulting single-eigenstate statistical mechanics. We then focus on a class of systems that fail to quantum thermalize and whose eigenstates violate the ETH: These are the many-body Anderson-localized systems; their long-time properties are not captured by the conventional ensembles of quantum statistical mechanics. These systems can forever locally remember information about their local initial conditions and are thus of interest for possibilities of storing quantum information. We discuss key features of many-body localization (MBL) and review a phenomenology of the MBL phase. Single-eigenstate statistical mechanics within the MBL phase reveal dynamically stable ordered phases, and phase transitions among them, that are invisible to equilibrium statistical mechanics and can occur at high energy and low spatial dimensionality, where equilibrium ordering is forbidden.

arXiv:1404.0686•Annual Review of Condensed Matter Physics•Mar 1, 2015•2,489 citations

Efficient Representation of Fully Many-Body Localized Systems Using Tensor Networks

Thorsten B. Wahl, Arijeet Pal, Steven H. Simon

Many-body-localized (MBL) phases are an intriguing state of matter where quantum systems fail to thermalize and retain their initial conditions for an indefinite amount of time. A new proposal for how to mathematically encode the dynamics of large, one-dimensional MBL systems shows an exponential decrease in computational time for analyzing the energy spectrum.

arXiv:1609.01552•Physical Review X•May 8, 2017•63 citations
When a system thermalizes it loses all memory of its initial conditions. Even within a closed quantum system, subsystems usually thermalize using the rest of the system as a heat bath. Exceptions to quantum thermalization have been observed, but typically require inherent symmetries or noninteracting particles in the presence of static disorder. The prediction of many-body localization (MBL), in which disordered quantum systems can fail to thermalize despite strong interactions and high excitation energy, was therefore surprising and has attracted considerable theoretical attention. We experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmably random disorder to ten spins initialized far from equilibrium with respect to the Hamiltonian. Using experimental and numerical methods we observe the essential signatures of MBL: initial state memory retention, Poissonian distributed many-body energy level spacings, and evidence of long-time entanglement growth. Our platform can be scaled to more spins, where detailed modeling of MBL becomes impossible.
The low‐frequency response of systems near the many‐body localization phase transition, on either side of the transition, is dominated by contributions from rare regions that are locally “in the other phase”, i.e., rare localized regions in a system that is typically thermal, or rare thermal regions in a system that is typically localized. Rare localized regions affect the properties of the thermal phase, especially in one dimension, by acting as bottlenecks for transport and the growth of entanglement, whereas rare thermal regions in the localized phase act as local “baths” and dominate the low‐frequency response of the MBL phase. We review recent progress in understanding these rare‐region effects, and discuss some of the open questions associated with them: in particular, whether and in what circumstances a single rare thermal region can destabilize the many‐body localized phase. image
We numerically explore the many body localization (MBL) transition through the lens of the entanglement spectrum . While a direct transition from localization to thermalization is believed to be obtained in the thermodynamic limit (the exact details of which remain an open problem), in finite system sizes there exists an intermediate 'quantum critical' regime. Previous numerical investigations have explored the crossover from thermalization to criticality, and have used this to place a numerical lower bound on the critical disorder strength for MBL. A careful analysis of the high energy part of the entanglement spectrum (which contains universal information about the critical point) allows us to study the crossover from criticality to MBL, and we find evidence for such a crossover which could allow us to place a numerical upper bound on the critical disorder strength for MBL.
We review some recent developments in the statistical mechanics of isolated quantum systems. We provide a brief introduction to quantum thermalization, paying particular attention to the eigenstate thermalization hypothesis (ETH) and the resulting single-eigenstate statistical mechanics. We then focus on a class of systems that fail to quantum thermalize and whose eigenstates violate the ETH: These are the many-body Anderson-localized systems; their long-time properties are not captured by the conventional ensembles of quantum statistical mechanics. These systems can forever locally remember information about their local initial conditions and are thus of interest for possibilities of storing quantum information. We discuss key features of many-body localization (MBL) and review a phenomenology of the MBL phase. Single-eigenstate statistical mechanics within the MBL phase reveal dynamically stable ordered phases, and phase transitions among them, that are invisible to equilibrium statistical mechanics and can occur at high energy and low spatial dimensionality, where equilibrium ordering is forbidden.