Remarks on effects of projective phase on eigenstate thermalization hypothesis

Abstract

The existence of $p$-form symmetry in $(d+1)$-dimensional quantum field is known to always lead to the breakdown of the eigenstate thermalization hypothesis (ETH) for certain $(d-p)$-dimensional operators other than symmetry operators under some assumptions. The assumptions include the mixing of symmetry sectors within a given energy shell, which is rather challenging to verify because it requires information on the eigenstates in the middle of the spectrum. We reconsider this assumption from the viewpoint of projective representations to avoid this difficulty. In the case of ${\mathbb{Z}}_N$ symmetries, we can circumvent the difficulty by considering ${\mathbb{Z}}_N\times {\mathbb{Z}}_N$-symmetric theories with nontrivial projective phases, and perturbing the Hamiltonian while preserving one of the ${\mathbb{Z}}_N$ symmetries of our interest. We also perform numerical analyses for $(1+1)$-dimensional spin chains and the $(2+1)$-dimensional ${\mathbb{Z}}_2$ lattice gauge theory.

arXiv comment23 pages, 5 figures; v3: minor modifications, published version in PTEP

References in corpus (53)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Generalized Global Symmetries
• Coupling a QFT to a TQFT and Duality
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• Theta, Time Reversal, and Temperature
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization
• Generalized Thermalization in an Integrable Lattice System
• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• Finite-size scaling of eigenstate thermalization
• Higher Gauging and Non-invertible Condensation Defects
• Off-diagonal matrix elements of local operators in many-body quantum 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 within isolated spin-chain systems
• Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems
• Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
• Canonical Typicality of Energy Eigenstates of an Isolated Quantum System
• Subsystem ETH
• Anomalies of discrete symmetries in three dimensions and group cohomology
• On the Approach to Thermal Equilibrium of Macroscopic Quantum Systems
• Eigenstate thermalization in the two-dimensional transverse field Ising model: II. Off-diagonal matrix elements of observables
• Eigenstate thermalization and quantum chaos in the Holstein polaron model
• Anomalies of discrete symmetries in various dimensions and group cohomology
• Generalization of von Neumann's Approach to Thermalization
• Eigenstate Thermalization, Random Matrix Theory and Behemoths
• On thermality of CFT eigenstates
• Anomaly Obstructions to Symmetry Preserving Gapped Phases
• Numerical Large Deviation Analysis of Eigenstate Thermalization Hypothesis
• Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics
• What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
• Thermal equilibrium of a macroscopic quantum system in a pure state
• Typicality and thermality in 2d CFT
• Eigenstate Randomization Hypothesis: Why Does the Long-Time Average Equal the Microcanonical Average?
• Generalized Eigenstate Thermalization in 2d CFTs
• Scars from protected zero modes and beyond in $U(1)$ quantum link and quantum dimer models
• Introduction to Generalized Global Symmetries in QFT and Particle Physics
• Comments on Thermalization in 2D CFT
• Off-Diagonal Observable Elements from Random Matrix Theory: Distributions, Fluctuations, and Eigenstate Thermalization
• Macroscopic and Microscopic Thermal Equilibrium
• Test of Eigenstate Thermalization Hypothesis Based on Local Random Matrix Theory
• Atypicality of Most Few-Body Observables
• Generalized Gibbs ensemble in a nonintegrable system with an extensive number of local symmetries
• Holographic Quantum Scars
• Quantum thermalization and Virasoro symmetry
• Random-matrix behavior of quantum nonintegrable many-body systems with Dyson's three symmetries
• Eigenstate thermalization hypothesis in two-dimensional XXZ model with or without SU(2) symmetry
• Anomalies and unnatural stability of multi-component Luttinger liquids in ${\mathbb{Z}}_n\times {\mathbb{Z}}_n$ spin chains
• Violation of Eigenstate Thermalization Hypothesis in Quantum Field Theories with Higher-Form Symmetry
• 't Hooft surface in lattice gauge theory
• Bounds on eigenstate thermalization
• On the Hellmann-Feynman theorem for degenerate states