On the boundary conformal field theory approach to symmetry-resolved entanglement

Giuseppe Di Giulio, René Meyer, Christian Northe, Henri Scheppach, Suting Zhao

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We study the symmetry resolution of the entanglement entropy of an interval in twodimensional conformal field theories (CFTs), by relating the bipartition to the geometry of an annulus with conformal boundary conditions. In the presence of extended symmetries such as Kac-Moody type current algebrae, symmetry resolution is possible only if the boundary conditions on the annulus preserve part of the symmetry group, i.e. if the factorization map associated with the spatial bipartition is compatible with the symmetry in question. The partition function of the boundary CFT (BCFT) is then decomposed in terms of the characters of the irreducible representations of the symmetry group preserved by the boundary conditions. We demonstrate that this decomposition already provides the symmetry resolution of the entanglement spectrum of the corresponding bipartition. Considering the various terms of the partition function associated with the same representation, or charge sector, the symmetry-resolved Rényi entropies can be derived to all orders in the UV cutoff expansion without the need to compute the charged moments. We apply this idea to the theory of a free massless boson with U(1), R and Z2 symmetry.

Original languageEnglish
Article number049
JournalSciPost Physics Core
Volume6
Issue number3
DOIs
StatePublished - 1 Jul 2023

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Atomic and Molecular Physics, and Optics
  • Nuclear and High Energy Physics
  • Condensed Matter Physics

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