The eigenstate thermalization hypothesis in constrained Hilbert spaces: a case study in non-Abelian anyon chains
arXiv:1607.00388 · doi:10.1103/PhysRevB.94.235122
Abstract
Many phases of matter, including superconductors, fractional quantum Hall fluids and spin liquids, are described by gauge theories with constrained Hilbert spaces. However, thermalization and the applicability of quantum statistical mechanics has primarily been studied in unconstrained Hilbert spaces. In this article, we investigate whether constrained Hilbert spaces permit local thermalization. Specifically, we explore whether the eigenstate thermalization hypothesis (ETH) holds in a pinned Fibonacci anyon chain, which serves as a representative case study. We first establish that the constrained Hilbert space admits a notion of locality, by showing that the influence of a measurement decays exponentially in space. This suggests that the constraints are no impediment to thermalization. We then provide numerical evidence that ETH holds for the diagonal and off-diagonal matrix elements of various local observables in a generic disorder-free non-integrable model. We also find that certain non-local observables obey ETH.
16 pages, 15 figures
References in corpus (26)
- Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
- Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
- Thermalization and its mechanism for generic isolated quantum systems
- Many body localization and thermalization in quantum statistical mechanics
- Localization of interacting fermions at high temperature
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Phenomenology of fully many-body-localized systems
- Experimental Observation of a Generalized Gibbs Ensemble
- Breakdown of thermalization in finite one-dimensional systems
- Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
- Interacting anyons in topological quantum liquids: The golden chain
- Exotic non-Abelian anyons from conventional fractional quantum Hall states
- Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
- Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
- Off-diagonal matrix elements of local operators in many-body quantum systems
- Eigenstate thermalization within isolated spin-chain systems
- Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
- Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
- A short introduction to Fibonacci anyon models
- Quantum chaos and thermalization in gapped systems
- Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit
- Quantum criticality of hot random spin chains
- Collective states of interacting Fibonacci anyons
- The quantum adiabatic algorithm and scaling of gaps at first order quantum phase transitions
- Strong-disorder renormalization for interacting non-Abelian anyon systems in two dimensions
- One-dimensional itinerant interacting non-Abelian anyons
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