Multi-charged moments and symmetry-resolved Rényi entropy of free compact boson for multiple disjoint intervals

Abstract

We study multi-charged moments and symmetry-resolved Rényi entropy of free compact boson for multiple disjoint intervals. The Rényi entropy evaluation involves computing the partition function of the theory on Riemann surfaces with genus g>1. This makes Rényi entropy sensitive to the local conformal algebra of the theory. The free compact boson possesses a global U(1) symmetry with respect to which we resolve Rényi entropy. The multi-charged moments are obtained by studying the correlation function of flux-generating vertex operators on the associated Riemann surface. Symmetry-resolved Rényi entropy is then obtained from the Fourier transforms of the charged moments. Rényi entropy is shown to have the familiar equipartition into local charge sectors up to the leading order. The multi-charged moments are also essential in studying the symmetry resolution of mutual information. The multi-charged moments of the self-dual compact boson and massless Dirac fermion are also shown to match for the cases when the associated reduced density matrix moments are known to be the same. Finally, we numerically check our results against the tight-binding model.

30 pages, 12 figures

References in corpus (25)

• Entanglement negativity in quantum field theory
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• 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
• Entanglement equipartition in critical random spin chains
• Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach
• Symmetry resolved entanglement: Exact results in 1D and beyond
• Symmetry decomposition of negativity of massless free fermions
• Symmetry resolved entanglement in two-dimensional systems via dimensional reduction
• Entanglement barrier and its symmetry resolution: theory and experiment
• Symmetry-Resolved Entanglement in AdS${}_3$/CFT${}_2$ coupled to $U(1)$ Chern-Simons Theory
• Finite-size corrections in critical symmetry-resolved entanglement
• Symmetry-resolved entanglement for excited states and two entangling intervals in AdS${}_3$/CFT${}_2$
• Bose-Fermi duality and entanglement entropies
• Symmetry decomposition of relative entropies in conformal field theory
• Charged Moments in $W_3$ Higher Spin Holography
• Entanglement of the $3$-State Potts Model via Form Factor Bootstrap: Total and Symmetry Resolved Entropies
• Charged Rényi negativity of massless free bosons
• Symmetry-resolved Entanglement Entropy, Spectra & Boundary Conformal Field Theory
• Entanglement resolution of free Dirac fermions on a torus
• Symmetry-resolved modular correlation functions in free fermionic theories
• Full counting statistics and symmetry resolved entanglement for free conformal theories with interface defects
• Charge imbalance resolved Rényi negativity for free compact boson: Two disjoint interval case
• Rényi entropy and negativity for massless complex boson at conformal interfaces and junctions
• Symmetry Resolved Entanglement Entropy in Hyperbolic de Sitter Space

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• Symmetry Resolved Measures in Quantum Field Theory: a Short Review
• Symmetry Resolution in non-Lorentzian Field Theories
• Non-abelian symmetry-resolved entanglement entropy
• On symmetry-resolved generalized entropies
• Total and Symmetry resolved Entanglement spectra in some Fermionic CFTs from the BCFT approach
• $2$-Rényi CCNR Negativity of Compact Boson for multiple disjoint intervals