Perturbative instability of nonergodic phases in non-Abelian quantum chains

Ware, Brayden; Abanin, Dmitry; Vasseur, Romain

doi:10.1103/physrevb.103.094203

Perturbative instability of nonergodic phases in non-Abelian quantum chains

Journal Article · Thu Mar 25 00:00:00 EDT 2021 · Physical Review B

DOI:https://doi.org/10.1103/physrevb.103.094203· OSTI ID:1772926

^[1]; Abanin, Dmitry ^[2]; Vasseur, Romain ^[3]

Univ. of Massachusetts, Amherst, MA (United States); UMass Amherst
Univ. of Geneva (Switzerland)
Univ. of Massachusetts, Amherst, MA (United States)

An important challenge in the field of many-body quantum dynamics is to identify nonergodic states of matter beyond many-body localization (MBL). Strongly disordered spin chains with non-Abelian symmetry and chains of non-Abelian anyons are natural candidates, as they are incompatible with standard MBL. In such chains, real space renormalization group methods predict a partially localized, nonergodic regime known as a quantum critical glass (a critical variant of MBL). Here, this regime features a treelike hierarchy of integrals of motion and symmetric eigenstates with entanglement entropy that scales as a logarithmically enhanced area law. We argue that such tentative nonergodic states are perturbatively unstable using an analytic computation of the scaling of off-diagonal matrix elements and accessible level spacing of local perturbations. Our results indicate that strongly disordered chains with non-Abelian symmetry display either spontaneous symmetry breaking or ergodic thermal behavior at long times. We identify the relevant length and timescales for thermalization: Even if such chains eventually thermalize, they can exhibit nonergodic dynamics up to parametrically long timescales with a nonanalytic dependence on disorder strength.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Massachusetts, Amherst, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0019168

OSTI ID:: 1772926

Journal Information:: Physical Review B, Journal Name: Physical Review B Journal Issue: 9 Vol. 103; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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