Perturbative instability of non-ergodic phases in non-Abelian quantum chains

Abstract

An important challenge in the field of many-body quantum dynamics is to identify non-ergodic 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, non-ergodic regime known as a quantum critical glass (a critical variant of MBL). This regime features a tree-like hierarchy of integrals of motion and symmetric eigenstates with entanglement entropy that scales as a logarithmically enhanced area law. We argue that such tentative non-ergodic 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 time scales for thermalization: even if such chains eventually thermalize, they can exhibit non-ergodic dynamics up to parametrically long time scales with a non-analytic dependence on disorder strength.

16 pages, 5 figures

References in corpus (19)

• Non-Abelian Anyons and Topological Quantum Computation
• Many body localization and thermalization in quantum statistical mechanics
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• Integrals of motion in the Many-Body localized phase
• Interacting anyons in topological quantum liquids: The golden chain
• Constructing local integrals of motion in the many-body localized phase
• How a small quantum bath can thermalize long localized chains
• Can we study the many-body localisation transition?
• A short introduction to Fibonacci anyon models
• Quantum criticality of hot random spin chains
• Renormalization-group study of the many-body localization transition in one dimension
• Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit
• Many-body localization near the critical point
• Emergent ergodicity at the transition between many-body localized phases
• Eigenstate phases with finite on-site non-Abelian symmetry
• One-dimensional itinerant interacting non-Abelian anyons
• Perturbative instability towards delocalization at phase transitions between MBL phases
• Universal crossover from ground state to excited-state quantum criticality

Cited by in corpus (7)

• Quantum information spreading in random spin chains
• Infinite randomness with continuously varying critical exponents in the random XYZ spin chain
• Finite-size subthermal regime in disordered SU(N)-symmetric Heisenberg chains
• Renormalization view on resonance proliferation between many-body localized phases
• Modelling sample-to-sample fluctuations of the gap ratio in finite disordered spin chains
• Anomalies of global symmetries on the lattice
• Relaxation mechanisms in a disordered system with the Poisson level statistics