We study the eigenstate phases of disordered spin chains with on-site finite non-Abelian symmetry. We develop a general formalism based on standard group theory to construct local spin Hamiltonians invariant under any on-site symmetry. We then specialize to the case of the simplest non-Abelian group, ${S}_{3}$ , and numerically study a particular two-parameter spin-1 Hamiltonian. We observe a thermal phase and a many-body localized phase with a spontaneous symmetry breaking (SSB) from ${S}_{3}$ to ${\mathbb{Z}}_{3}$ in our model Hamiltonian. We diagnose these phases using full entanglement distributions and level statistics. We also use a spin-glass diagnostic specialized to detect spontaneous breaking of the ${S}_{3}$ symmetry down to ${\mathbb{Z}}_{3}$ . Our observed phases are consistent with the possibilities outlined by A. C. Potter and R. Vasseur [Phys. Rev. B 94, 224206 (2016)], namely thermal/ergodic and many-body-localized spin-glass (MBL-SG) phases. We also speculate on the nature of an intermediate region between the thermal and MBL + SSB regions where full ${S}_{3}$ symmetry exists.We study the eigenstate phases of disordered spin chains with on-site finite non-Abelian symmetry. We develop a general formalism based on standard group theory to construct local spin Hamiltonians invariant under any on-site symmetry. We then specialize to the case of the simplest non-Abelian group, ${S}_{3}$, and numerically study a particular two-parameter spin-1 Hamiltonian. We observe a thermal phase and a many-body localized phase with a spontaneous symmetry breaking (SSB) from ${S}_{3}$ to ${\mathbb{Z}}_{3}$ in our model Hamiltonian. We diagnose these phases using full entanglement distributions and level statistics. We also use a spin-glass diagnostic specialized to detect spontaneous breaking of the ${S}_{3}$ symmetry down to ${\mathbb{Z}}_{3}$. Our observed phases are consistent with the possibilities outlined by A. C. Potter and R. Vasseur [Phys. Rev. B 94, 224206 (2016)], namely thermal/ergodic and many-body-localized spin-glass (MBL-SG) phases. We also speculate on the nature of an intermediate region between the thermal and MBL + SSB regions where full ${S}_{3}$ symmetry exists.

arXiv:1706.06062Physical review. B./Physical review. BOct 18, 201718 citations

Breaking of Ergodicity in Disordered Systems: The Case of Spin Glasses

G. Toulouse

Springer series in solid-state sciencesJan 1, 19821 citation

Perturbative instability of nonergodic phases in non-Abelian quantum chains

Brayden Ware, Dmitry A. Abanin, Romain Vasseur

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). 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.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). 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.

arXiv:2010.10550Physical review. B./Physical review. BMar 25, 20217 citations

{S}_{3}

, and numerically study a particular two-parameter spin-1 Hamiltonian. We observe a thermal phase and a many-body localized phase with a spontaneous symmetry breaking (SSB) from

{S}_{3}

{\mathbb{Z}}_{3}

in our model Hamiltonian. We diagnose these phases using full entanglement distributions and level statistics. We also use a spin-glass diagnostic specialized to detect spontaneous breaking of the

{S}_{3}

symmetry down to

{\mathbb{Z}}_{3}

. Our observed phases are consistent with the possibilities outlined by A. C. Potter and R. Vasseur [Phys. Rev. B 94, 224206 (2016)], namely thermal/ergodic and many-body-localized spin-glass (MBL-SG) phases. We also speculate on the nature of an intermediate region between the thermal and MBL + SSB regions where full

{S}_{3}

symmetry exists.