Symmetry-Resolved Entanglement: General considerations, calculation from correlation functions, and bounds for symmetry-protected topological phases

Abstract

We discuss some general properties of the symmetry-resolved von-Neumann entanglement entropy in systems with particle number conservation and describe how to obtain the entanglement components from correlation functions for Gaussian systems. We introduce majorization as an important tool to derive entanglement bounds. As an application, we derive lower bounds both for the number and the configurational entropy for chiral and Cn-symmetric topological phases. In some cases, our considerations also lead to an improvement of the previously known lower bounds for the entanglement entropy in such systems.

arXiv comment20 pages

References in corpus (32)

• Classification of topological quantum matter with symmetries
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Calculation of reduced density matrices from correlation functions
• Inversion Symmetric Topological Insulators
• Probing entanglement in a many-body-localized system
• The entanglement of indistinguishable particles shared between two parties
• Quantum Noise as an Entanglement Meter
• Symmetry-resolved entanglement in many-body systems
• Evidence for unbounded growth of the number entropy in many-body localized phases
• Equipartition of the Entanglement Entropy
• Absence of true localization in many-body localized phases
• Symmetry resolved entanglement in free fermionic systems
• Quasiparticle dynamics of symmetry resolved entanglement after a quench: the examples of conformal field theories and free fermions
• Entanglement and symmetry resolution in two dimensional free quantum field theories
• Rényi generalization of the operational entanglement entropy
• Entanglement equipartition in critical random spin chains
• Symmetry-resolved dynamical purification in synthetic quantum matter
• Operationally accessible entanglement of one dimensional spinless fermions
• Symmetry decomposition of negativity of massless free fermions
• Symmetry resolved entanglement in integrable field theories via form factor bootstrap
• Entanglement Spectrum Classification of $C_n$-invariant Noninteracting Topological Insulators in Two Dimensions
• Symmetry-resolved entanglement in symmetry-protected topological phases
• Boundary effects on symmetry resolved entanglement
• Operational Entanglement of Symmetry-Protected Topological Edge States
• Bounds on the entanglement entropy by the number entropy in non-interacting fermionic systems
• Equipartition of Entanglement in Quantum Hall States
• A proof of the Shepp-Olkin entropy concavity conjecture
• Charge-resolved entanglement in the presence of topological defects
• Symmetry-resolved entanglement of 2D symmetry-protected topological states
• Symmetry-Resolved Entanglement of $C_2$-symmetric Topological Insulators
• Tunable mode entanglement: topological Su-Schrieffer-Heeger (SSH) chain with an embedded Aharonov-Bohm quantum ring
• Entanglement and particle fluctuations of one-dimensional chiral topological insulators

Cited by in corpus (7)

• Symmetry Resolved Measures in Quantum Field Theory: a Short Review
• Noninvertible Symmetry-Resolved Affleck-Ludwig-Cardy Formula and Entanglement Entropy from the Boundary Tube Algebra
• Hidden zero modes and topology of multiband non-Hermitian systems
• Exceptional Points, Bulk-Boundary Correspondence, and Entanglement Properties for a Dimerized Hatano-Nelson Model with Staggered Potentials
• Disentangling the Physics of the Attractive Hubbard Model via the Accessible and Symmetry-Resolved Entanglement Entropies
• Topological Properties of Single-Particle States Decaying into a Continuum due to Interaction
• Bulk-boundary correspondence in topological two-dimensional non-Hermitian systems: Toeplitz operators and singular values