Thermalization and Many-body Localization

Many-body localized (MBL) systems fail to reach thermal equilibrium under their own dynamics, even though they are interacting, nonintegrable, and in an extensively excited state. One instability toward thermalization of MBL systems is the so-called "avalanche," where a locally thermalizing rare region is able to spread thermalization through the full system. The spreading of the avalanche may be modeled and numerically studied in finite one-dimensional MBL systems by weakly coupling an infinite-temperature bath to one end of the system. We find that the avalanche spreads primarily via strong many-body resonances between rare near-resonant eigenstates of the closed system. Thus we find and explore a detailed connection between many-body resonances and avalanches in MBL systems.Many-body localized (MBL) systems fail to reach thermal equilibrium under their own dynamics, even though they are interacting, nonintegrable, and in an extensively excited state. One instability toward thermalization of MBL systems is the so-called "avalanche," where a locally thermalizing rare region is able to spread thermalization through the full system. The spreading of the avalanche may be modeled and numerically studied in finite one-dimensional MBL systems by weakly coupling an infinite-temperature bath to one end of the system. We find that the avalanche spreads primarily via strong many-body resonances between rare near-resonant eigenstates of the closed system. Thus we find and explore a detailed connection between many-body resonances and avalanches in MBL systems.

arXiv:2301.04658Physical Review LettersJun 23, 202332 citations

Thermalization in 1d many body systems

I. E. Mazets, Jörg Schmiedmayer

Bulletin of the American Physical SocietyMay 29, 20100 citations

Avalanches and many-body resonances in many-body localized systems

Alan Morningstar, Luis Colmenárez, Vedika Khemani +2 more

Many-body localization (MBL) is a mechanism by which quantum chains with strong enough disorder can avoid thermalization. Here, the authors define and locate several distinct landmarks having to do with thermalization, rare many-body resonances, and so-called thermal avalanches in systems that can exhibit MBL. These landmarks are well separated in the strength of the disorder, and the estimate of where MBL breaks down in asymptotically large systems is far beyond what is usually pointed to as the MBL transition.Many-body localization (MBL) is a mechanism by which quantum chains with strong enough disorder can avoid thermalization. Here, the authors define and locate several distinct landmarks having to do with thermalization, rare many-body resonances, and so-called thermal avalanches in systems that can exhibit MBL. These landmarks are well separated in the strength of the disorder, and the estimate of where MBL breaks down in asymptotically large systems is far beyond what is usually pointed to as the MBL transition.

arXiv:2107.05642Physical review. B./Physical review. BMay 12, 2022257 citations

Many-body localization

Arijeet Pal

Jan 1, 201210 citations

Many-body localization with quasiperiodic driving

David M. Long, Philip J. D. Crowley, Anushya Chandran

Sufficient disorder is believed to localize static and periodically driven interacting chains. With quasiperiodic driving by $D$ incommensurate tones, the fate of this many-body localization (MBL) is unknown. We argue that randomly disordered MBL exists for $D=2$ , but not for $D\ensuremath{\ge}3$. Specifically, a putative two-tone driven MBL chain is neither destabilized by thermal avalanches seeded by rare thermal regions, nor by the proliferation of long-range many-body resonances. For $D\ensuremath{\ge}3$, however, sufficiently large thermal regions have continuous local spectra and slowly thermalize the entire chain. En route, we generalize the eigenstate thermalization hypothesis to the quasiperiodically driven setting, and we verify its predictions numerically. Two-tone driving enables new topological orders with edge signatures; our results suggest that localization protects these orders indefinitely.Sufficient disorder is believed to localize static and periodically driven interacting chains. With quasiperiodic driving by $D$ incommensurate tones, the fate of this many-body localization (MBL) is unknown. We argue that randomly disordered MBL exists for $D=2$, but not for $D\ensuremath{\ge}3$. Specifically, a putative two-tone driven MBL chain is neither destabilized by thermal avalanches seeded by rare thermal regions, nor by the proliferation of long-range many-body resonances. For $D\ensuremath{\ge}3$, however, sufficiently large thermal regions have continuous local spectra and slowly thermalize the entire chain. En route, we generalize the eigenstate thermalization hypothesis to the quasiperiodically driven setting, and we verify its predictions numerically. Two-tone driving enables new topological orders with edge signatures; our results suggest that localization protects these orders indefinitely.

arXiv:2108.04834Physical review. B./Physical review. BApr 19, 202229 citations

Sufficient disorder is believed to localize static and periodically driven interacting chains. With quasiperiodic driving by

D

incommensurate tones, the fate of this many-body localization (MBL) is unknown. We argue that randomly disordered MBL exists for

D=2

, but not for $D\ensuremath{\ge}3$. Specifically, a putative two-tone driven MBL chain is neither destabilized by thermal avalanches seeded by rare thermal regions, nor by the proliferation of long-range many-body resonances. For $D\ensuremath{\ge}3$, however, sufficiently large thermal regions have continuous local spectra and slowly thermalize the entire chain. En route, we generalize the eigenstate thermalization hypothesis to the quasiperiodically driven setting, and we verify its predictions numerically. Two-tone driving enables new topological orders with edge signatures; our results suggest that localization protects these orders indefinitely.