TY - JOUR

T1 - Entanglement-Ergodic Quantum Systems Equilibrate Exponentially Well

AU - Wilming, H.

AU - Goihl, M.

AU - Roth, I.

AU - Eisert, J.

N1 - Funding Information: H. W. would like to thank Rodrigo Gallego for fruitful discussions regarding the role of Rényi entropies in equilibration. We acknowledge financial support from the ERC (TAQ), the DFG (FOR 2724, CRC 183, EI 519/7-1, EI 519/9-1), the Templeton Foundation, and the Studienstiftung des Deutschen Volkes. H. W. further acknowledges contributions from the Swiss National Science Foundation via the NCCR QSIT as well as Project No. 200020_165843. This work has also received funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No. 817482 (PASQuanS).

PY - 2019/11/13

Y1 - 2019/11/13

N2 - One of the outstanding problems in nonequilibrium physics is to precisely understand when and how physically relevant observables in many-body systems equilibrate under unitary time evolution. General equilibration results show that equilibration is generic provided that the initial state has overlap with sufficiently many energy levels. But results not referring to typicality which show that natural initial states actually fulfill this condition are lacking. In this work, we present stringent results for equilibration for systems in which Rényi entanglement entropies in energy eigenstates with finite energy density are extensive for at least some, not necessarily connected, subsystems. Our results reverse the logic of common arguments, in that we derive equilibration from a weak condition akin to the eigenstate thermalization hypothesis, which is usually attributed to thermalization in systems that are assumed to equilibrate in the first place. We put the findings into the context of studies of many-body localization and many-body scars.

AB - One of the outstanding problems in nonequilibrium physics is to precisely understand when and how physically relevant observables in many-body systems equilibrate under unitary time evolution. General equilibration results show that equilibration is generic provided that the initial state has overlap with sufficiently many energy levels. But results not referring to typicality which show that natural initial states actually fulfill this condition are lacking. In this work, we present stringent results for equilibration for systems in which Rényi entanglement entropies in energy eigenstates with finite energy density are extensive for at least some, not necessarily connected, subsystems. Our results reverse the logic of common arguments, in that we derive equilibration from a weak condition akin to the eigenstate thermalization hypothesis, which is usually attributed to thermalization in systems that are assumed to equilibrate in the first place. We put the findings into the context of studies of many-body localization and many-body scars.

UR - http://www.scopus.com/inward/record.url?scp=85075113134&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.123.200604

DO - 10.1103/PhysRevLett.123.200604

M3 - Article

C2 - 31809071

AN - SCOPUS:85075113134

VL - 123

JO - Physical review letters

JF - Physical review letters

SN - 0031-9007

IS - 20

M1 - 200604

ER -