Ergodicity and symmetry breaking in disordered spin chains with on-site non-Abelian symmetry

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

Interplay between symmetry breaking and quasiperiodicity in spin chains

Indubala I. Satija, Bala Sundaram

Il Nuovo Cimento DJul 1, 19961 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.