Avalanches and many-body resonances in many-body localized systems
Abstract
Here we numerically study both the avalanche instability and many-body resonances in strongly disordered spin chains exhibiting many-body localization (MBL). Finite-size systems behave like MBL within the MBL regimes, which we divide into the asymptotic MBL phase and the finite-size MBL regime; the latter regime is, however, thermal in the limit of large systems and long times. In both Floquet and Hamiltonian models, we identify some landmarks within the MBL regimes. Our first landmark is an estimate of where the MBL phase becomes unstable to avalanches, obtained by measuring the slowest relaxation rate of a finite chain coupled to an infinite bath at one end. Our estimates indicate that the actual MBL-to-thermal phase transition occurs much deeper in the MBL regimes than has been suggested by most previous studies. Our other landmarks involve systemwide many-body resonances: We find that the effective matrix elements producing eigenstates with systemwide many-body resonances are enormously broadly distributed. This broad distribution means that the onset of such resonances in typical samples occurs quite deep in the MBL regimes, and the first such resonances typically involve rare pairs of eigenstates that are farther apart in energy than the minimum gap. Thus we find that the resonancemore »
- Authors:
-
[1];
[2];
[5]
- Princeton University, NJ (United States)
- Max Planck Institute for the Physics of Complex Systems, Dresden (Germany)
- Stanford University, CA (United States)
- University of Bonn (Germany); Max Planck Institute for the Physics of Complex Systems, Dresden (Germany)
- Princeton University, NJ (United States); Institute for Advanced Study, Princeton, NJ (United States)
- Publication Date:
- Research Org.:
- Stanford Univ., CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); German Research Foundation (DFG)
- OSTI Identifier:
- 1979752
- Alternate Identifier(s):
- OSTI ID: 2301798
- Grant/Contract Number:
- SC0021111
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 105; Journal Issue: 17; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; many-body localization; phase transitions; quantum statistical mechanics; quantum many-body systems
Citation Formats
Morningstar, Alan, Colmenarez, Luis, Khemani, Vedika, Luitz, David J., and Huse, David A. Avalanches and many-body resonances in many-body localized systems. United States: N. p., 2022.
Web. doi:10.1103/physrevb.105.174205.
Morningstar, Alan, Colmenarez, Luis, Khemani, Vedika, Luitz, David J., & Huse, David A. Avalanches and many-body resonances in many-body localized systems. United States. https://doi.org/10.1103/physrevb.105.174205
Morningstar, Alan, Colmenarez, Luis, Khemani, Vedika, Luitz, David J., and Huse, David A. Thu .
"Avalanches and many-body resonances in many-body localized systems". United States. https://doi.org/10.1103/physrevb.105.174205. https://www.osti.gov/servlets/purl/1979752.
@article{osti_1979752,
title = {Avalanches and many-body resonances in many-body localized systems},
author = {Morningstar, Alan and Colmenarez, Luis and Khemani, Vedika and Luitz, David J. and Huse, David A.},
abstractNote = {Here we numerically study both the avalanche instability and many-body resonances in strongly disordered spin chains exhibiting many-body localization (MBL). Finite-size systems behave like MBL within the MBL regimes, which we divide into the asymptotic MBL phase and the finite-size MBL regime; the latter regime is, however, thermal in the limit of large systems and long times. In both Floquet and Hamiltonian models, we identify some landmarks within the MBL regimes. Our first landmark is an estimate of where the MBL phase becomes unstable to avalanches, obtained by measuring the slowest relaxation rate of a finite chain coupled to an infinite bath at one end. Our estimates indicate that the actual MBL-to-thermal phase transition occurs much deeper in the MBL regimes than has been suggested by most previous studies. Our other landmarks involve systemwide many-body resonances: We find that the effective matrix elements producing eigenstates with systemwide many-body resonances are enormously broadly distributed. This broad distribution means that the onset of such resonances in typical samples occurs quite deep in the MBL regimes, and the first such resonances typically involve rare pairs of eigenstates that are farther apart in energy than the minimum gap. Thus we find that the resonance properties define two landmarks that divide the MBL regimes of finite-size systems into three subregimes: (i) at strongest randomness, typical samples do not have any eigenstates that are involved in systemwide many-body resonances; (ii) there is a substantial intermediate subregime where typical samples do have such resonances but the pair of eigenstates with the minimum spectral gap does not, so the size of the minimum gap agrees with expectations from Poisson statistics; and (iii) in the weaker randomness subregime, the minimum gap is larger than predicted by Poisson level statistics because it is involved in a many-body resonance and thus subject to level repulsion. Nevertheless, even in this third subregime, all but a vanishing fraction of eigenstates remain nonresonant and the system thus still appears MBL in most respects. Based on our estimates of the location of the avalanche instability, it might be that the MBL phase is only part of subregime (i) and the other subregimes are entirely in the thermal phase, even though they look localized in most respects, so are in the finite-size MBL regime.},
doi = {10.1103/physrevb.105.174205},
journal = {Physical Review. B},
number = 17,
volume = 105,
place = {United States},
year = {Thu May 12 00:00:00 EDT 2022},
month = {Thu May 12 00:00:00 EDT 2022}
}
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Works referencing / citing this record:
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