Entanglement Spectrum Resolved by Loop Symmetries
arXiv:2510.18350 · doi:10.1103/gsml-klfg
Abstract
A rigorous analysis is presented for the entanglement spectrum of quantum many-body states possessing a higher-form group-representation symmetry generated by topological Wilson loops, which is generally non-invertible. A general framework based on elementary algebraic topology and category theory is developed to determine the block structure of reduced density matrices for arbitrary bipartite manifolds on which the states are defined. Within this framework, we scrutinize the impact of topology on the entanglement structure for low-dimensional manifolds, including especially the torus, the Klein bottle, and lens spaces. By further incorporating gauge invariance, we refine our framework to determine the entanglement structure for topological gauge theories in arbitrary dimensions. In particular, in two dimensions, it is shown for the Kitaev quantum double model that not only the topological entanglement entropy can be reproduced, but also the Li-Haldane conjecture concerning the full entanglement spectrum holds exactly.
18+32 pages, 5+8 figures. Comments welcome!
References in corpus (53)
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Entanglement Entropy and Quantum Field Theory
- Area laws for the entanglement entropy - a review
- Entanglement in quantum critical phenomena
- Topological entanglement entropy
- Detecting topological order in a ground state wave function
- Many-body localization, thermalization, and entanglement
- Generalized Global Symmetries
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- Entanglement spectrum of a topological phase in one dimension
- Zoo of quantum-topological phases of matter
- Quantum entanglement in condensed matter systems
- Notes on Some Entanglement Properties of Quantum Field Theory
- Coupling a QFT to a TQFT and Duality
- Jerusalem Lectures on Black Holes and Quantum Information
- Entanglement spectrum of topological insulators and superconductors
- TFT construction of RCFT correlators I: Partition functions
- Generalized Symmetries in Condensed Matter
- Quasi-particle Statistics and Braiding from Ground State Entanglement
- Entanglement entropy: holography and renormalization group
- Symmetry-resolved entanglement in many-body systems
- Topological Defects on the Lattice I: The Ising model
- Topological Entanglement Entropy in Chern-Simons Theories and Quantum Hall Fluids
- Equipartition of the Entanglement Entropy
- Universal Non-Invertible Symmetries
- Finite Group Modular Data
- Many body localization and thermalization: insights from the entanglement spectrum
- Symmetry resolved entanglement in free fermionic systems
- Entanglement Entropy of Gapped Phases and Topological Order in Three dimensions
- Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
- TFT construction of RCFT correlators II: Unoriented world sheets
- Unifying Constructions of Non-Invertible Symmetries
- Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies
- On lattice models of gapped phases with fusion category symmetries
- Cluster state as a non-invertible symmetry protected topological phase
- Fracton phases via exotic higher-form symmetry-breaking
- More on time-reversal anomaly of 2+1d topological phases
- A new multi-partite entanglement measure and its holographic dual
- Exact emergent higher-form symmetries in bosonic lattice models
- Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
- Anyonic Entanglement and Topological Entanglement Entropy
- Mixed-state quantum anomaly and multipartite entanglement
- Universal lower bound on topological entanglement entropy
- Physics of Symmetry Protected Topological phases involving Higher Symmetries and their Applications
- The triviality problem for profinite completions
- Entanglement Properties of Gauge Theories from Higher-Form Symmetries
- Violation of Eigenstate Thermalization Hypothesis in Quantum Field Theories with Higher-Form Symmetry
- Multi wavefunction overlap and multi entropy for topological ground states in (2+1) dimensions
- Categorical-Symmetry Resolved Entanglement in CFT
- Topological Entanglement Entropy in \(d\)-dimensions for Abelian Higher Gauge Theories
- Problems around 3-manifolds
- On dimensions of (2+1)D abelian bosonic topological systems on non-orientable manifolds
- Threefold Way for Typical Entanglement