Relating the entanglement spectrum of noninteracting band insulators to their quantum geometry and topology

Abstract

We study the entanglement spectrum of noninteracting band insulators, which can be computed from the two-point correlation function, when restricted to one part of the system. In particular, we analyze a type of partitioning of the system that maintains its full translational symmetry, by tracing over a subset of local degrees of freedom, such as sublattice sites or spin orientations. The corresponding single-particle entanglement spectrum is the band structure of an entanglement Hamiltonian in the Brillouin zone. We find that the hallmark of a nontrivial topological phase is a gapless entanglement spectrum with an "entanglement Fermi surface." Furthermore, we derive a relation between the entanglement spectrum and the quantum geometry of Bloch states contained in the Fubini-Study metric. The results are illustrated with lattice models of Chern insulators and Z_2 topological insulators.

10 pages, 4 figures

References in corpus (3)

• Classification of topological insulators and superconductors in three spatial dimensions
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Abelian and Non-Abelian Quantum Geometric Tensor

Cited by in corpus (22)

• Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice
• Extracting the quantum metric tensor through periodic driving
• Semi-classical wave packet dynamics in non-uniform electric fields
• Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations
• Topological Quantum Liquids with Long-Range Couplings
• Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions
• Steady-state Hall response and quantum geometry of driven-dissipative lattices
• Topological and non-topological features of generalized Su-Schrieffer-Heeger models
• Signatures of metal-insulator and topological phase transitions in the entanglement of one-dimensional disordered fermions
• Symmetry-protected entangling boundary zero modes in crystalline topological insulators
• Detection of Chern numbers and entanglement in topological two-species systems through subsystem winding numbers
• Extracting non-Abelian quantum metric tensor and its related Chern numbers
• Entanglement spectrum and entropy in Floquet topological matter
• Non-Abelian quantum geometric tensor in degenerate topological semimetals
• Geometric entanglement in integer quantum Hall states
• Entanglement conductance as a characterization of delocalized-localized phase transition in free fermion models
• Sensitivity of the entanglement spectrum to boundary conditions as a characterization of the phase transition from delocalization to localization
• A topological classification of molecules and chemical reactions with a perplectic structure
• Invariance of topological indices under Hilbert space truncation
• Dissipation-driven topological phase transitions in open quantum systems independent of system Hamiltonian
• Refined Characterization of Lattice Chern Insulators by Bulk Entanglement Spectrum
• Extended edge modes and disorder preservation of a symmetry-protected topological phase out of equilibrium