We study the symmetry resolved entanglement entropies in one-dimensional systems with boundaries. We provide some general results for conformal invariant theories and then move to a semi-infinite chain of free fermions. We consider both an interval starting from the boundary and away from it. We derive exact formulas for the charged and symmetry resolved entropies based on theorems and conjectures about the spectra of Toeplitz+Hankel matrices. En route to characterise the interval away from the boundary, we prove a general relation between the eigenvalues of Toeplitz+Hankel matrices and block Toeplitz ones. An important aspect is that the saddle-point approximation from charged to symmetry resolved entropies introduces algebraic corrections to the scaling that are much more severe than in systems without boundaries.

Boundary effects on symmetry resolved entanglement / Bonsignori, R.; Calabrese, P.. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 54:1(2021), p. 015005. [10.1088/1751-8121/abcc3a]

Boundary effects on symmetry resolved entanglement

Bonsignori R.;Calabrese P.
2021

Abstract

We study the symmetry resolved entanglement entropies in one-dimensional systems with boundaries. We provide some general results for conformal invariant theories and then move to a semi-infinite chain of free fermions. We consider both an interval starting from the boundary and away from it. We derive exact formulas for the charged and symmetry resolved entropies based on theorems and conjectures about the spectra of Toeplitz+Hankel matrices. En route to characterise the interval away from the boundary, we prove a general relation between the eigenvalues of Toeplitz+Hankel matrices and block Toeplitz ones. An important aspect is that the saddle-point approximation from charged to symmetry resolved entropies introduces algebraic corrections to the scaling that are much more severe than in systems without boundaries.
54
1
015005
https://arxiv.org/abs/2009.08508
Bonsignori, R.; Calabrese, P.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/117217
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 24
  • ???jsp.display-item.citation.isi??? 25
social impact