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:1611.00770 · Annalen der Physik

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

Kartiek Agarwal, Ehud Altman, Eugene Demler, Sarang Gopalakrishnan, David A. Huse, Michael Knap

Published Jan 12, 2017• 211 citations
arXivHTMLPDF

Abstract

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

DOI
10.1002/andp.201600326

Related papers

Griffiths effects and slow dynamics in nearly many-body localized systems

Sarang Gopalakrishnan, Kartiek Agarwal, Eugene Demler +2 more

The low-frequency response of systems near a many-body localization transition can be dominated by rare regions that are locally critical or ``in the other phase.'' It is known that in one dimension, these rare regions can cause the dc conductivity and diffusion constant to vanish even inside the delocalized thermal phase. Here, we present a general analysis of such Griffiths effects in the thermal phase near the many-body localization transition: we consider both one-dimensional and higher-dimensional systems, subject to quenched randomness, and discuss both linear response (including the frequency- and wave-vector-dependent conductivity) and more general dynamics. In all the regimes we consider, we identify observables that are dominated by rare-region effects. In some cases (one-dimensional systems and Floquet systems with no extensive conserved quantities), essentially all long-time local observables are dominated by rare-region effects; in others, generic observables are instead dominated by hydrodynamic long-time tails throughout the thermal phase, and one must look at specific probes, such as spin echo, to see Griffiths behavior.

arXiv:1511.06389•Physical review. B./Physical review. B•Apr 11, 2016•150 citations

Large-deviation analysis of rare resonances for the many-body localization transition

Giulio Biroli, Alexander K. Hartmann, Marco Tarzia

The authors explore here the many-body localization (MBL) transition through a novel approach based on an analogy with directed polymers in random media. This study reveals how rare long-range resonances, typically absent in small samples, destabilize the MBL phase in the thermodynamic limit in a broad region of the phase diagram, and shift the transition to much higher disorder levels, offering new insights into quantum avalanches and anomalous transport and relaxation near the transition.

Physical review. B./Physical review. B•Jul 17, 2024•22 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

The ergodic side of the many‐body localization transition

David J. Luitz, Yevgeny Bar Lev

Recent studies point towards nontriviality of the ergodic phase in systems exhibiting many‐body localization (MBL), which shows subexponential relaxation of local observables, subdiffusive transport and sublinear spreading of the entanglement entropy. Here we review the dynamical properties of this phase and the available numerically exact and approximate methods for its study. We discuss in which sense this phase could be considered ergodic and present possible phenomenological explanations of its dynamical properties. We close by analyzing to which extent the proposed explanations were verified by numerical studies and present the open questions in this field. image

arXiv:1610.08993•Annalen der Physik•May 15, 2017•315 citations

Mean-field theory of nearly many-body localized metals

Sarang Gopalakrishnan, Rahul Nandkishore

We develop a mean-field theory of the metallic phase near the many-body localization (MBL) transition, using the observation that a system near the MBL transition should become an increasingly slow heat bath for its constituent parts. As a first step, we consider the properties of a many-body localized system coupled to a generic ergodic bath whose characteristic dynamical time scales are much slower than those of the system. As we discuss, a wide range of experimentally relevant systems fall into this class; we argue that relaxation in these systems is dominated by collective many-particle rearrangements, and compute the associated time scales and spectral broadening. We then use the observation that the self-consistent environment of any region in a nearly localized metal can itself be modeled as a slowly fluctuating bath to outline a self-consistent mean-field description of the nearly localized metal and the localization transition. In the nearly localized regime, the spectra of local operators are highly inhomogeneous and the typical local spectral linewidth is narrow. The local spectral linewidth is proportional to the dc conductivity, which is small in the nearly localized regime. This typical linewidth and the dc conductivity go to zero as the localized phase is approached, with a scaling that we calculate, and which appears to be in good agreement with recent experimental results.

arXiv:1405.1036•Physical Review B•Dec 29, 2014•63 citations

Low-frequency conductivity in many-body localized systems

Sarang Gopalakrishnan, Markus Müller, Vedika Khemani +3 more

We argue that the ac conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ in the many-body localized phase is a power law of frequency $\ensuremath{\omega}$ at low frequency: specifically, $\ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{\ensuremath{\alpha}}$ with the exponent $\ensuremath{\alpha}$ approaching 1 at the phase transition to the thermal phase, and asymptoting to 2 deep in the localized phase. We identify two separate mechanisms giving rise to this power law: deep in the localized phase, the conductivity is dominated by rare resonant pairs of configurations; close to the transition, the dominant contributions are rare regions that are locally critical or in the thermal phase. We present numerical evidence supporting these claims, and discuss how these power laws can also be seen through polarization-decay measurements in ultracold atomic systems.

arXiv:1502.07712•Physical Review B•Sep 11, 2015•195 citations
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
The low-frequency response of systems near a many-body localization transition can be dominated by rare regions that are locally critical or ``in the other phase.'' It is known that in one dimension, these rare regions can cause the dc conductivity and diffusion constant to vanish even inside the delocalized thermal phase. Here, we present a general analysis of such Griffiths effects in the thermal phase near the many-body localization transition: we consider both one-dimensional and higher-dimensional systems, subject to quenched randomness, and discuss both linear response (including the frequency- and wave-vector-dependent conductivity) and more general dynamics. In all the regimes we consider, we identify observables that are dominated by rare-region effects. In some cases (one-dimensional systems and Floquet systems with no extensive conserved quantities), essentially all long-time local observables are dominated by rare-region effects; in others, generic observables are instead dominated by hydrodynamic long-time tails throughout the thermal phase, and one must look at specific probes, such as spin echo, to see Griffiths behavior.
Recent studies point towards nontriviality of the ergodic phase in systems exhibiting many‐body localization (MBL), which shows subexponential relaxation of local observables, subdiffusive transport and sublinear spreading of the entanglement entropy. Here we review the dynamical properties of this phase and the available numerically exact and approximate methods for its study. We discuss in which sense this phase could be considered ergodic and present possible phenomenological explanations of its dynamical properties. We close by analyzing to which extent the proposed explanations were verified by numerical studies and present the open questions in this field. image
We develop a mean-field theory of the metallic phase near the many-body localization (MBL) transition, using the observation that a system near the MBL transition should become an increasingly slow heat bath for its constituent parts. As a first step, we consider the properties of a many-body localized system coupled to a generic ergodic bath whose characteristic dynamical time scales are much slower than those of the system. As we discuss, a wide range of experimentally relevant systems fall into this class; we argue that relaxation in these systems is dominated by collective many-particle rearrangements, and compute the associated time scales and spectral broadening. We then use the observation that the self-consistent environment of any region in a nearly localized metal can itself be modeled as a slowly fluctuating bath to outline a self-consistent mean-field description of the nearly localized metal and the localization transition. In the nearly localized regime, the spectra of local operators are highly inhomogeneous and the typical local spectral linewidth is narrow. The local spectral linewidth is proportional to the dc conductivity, which is small in the nearly localized regime. This typical linewidth and the dc conductivity go to zero as the localized phase is approached, with a scaling that we calculate, and which appears to be in good agreement with recent experimental results.
We argue that the ac conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ in the many-body localized phase is a power law of frequency $\ensuremath{\omega}$ at low frequency: specifically, $\ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{\ensuremath{\alpha}}$ with the exponent $\ensuremath{\alpha}$ approaching 1 at the phase transition to the thermal phase, and asymptoting to 2 deep in the localized phase. We identify two separate mechanisms giving rise to this power law: deep in the localized phase, the conductivity is dominated by rare resonant pairs of configurations; close to the transition, the dominant contributions are rare regions that are locally critical or in the thermal phase. We present numerical evidence supporting these claims, and discuss how these power laws can also be seen through polarization-decay measurements in ultracold atomic systems.