Multi-charged moments and symmetry-resolved R\'enyi entropy of free compact boson for multiple disjoint intervals

• URL: http://arxiv.org/abs/2310.14186v1
• Date: Sun, 22 Oct 2023 05:24:41 GMT
• Title: Multi-charged moments and symmetry-resolved R\'enyi entropy of free compact boson for multiple disjoint intervals
• Authors: Himanshu Gaur and Urjit A. Yajnik
• Abstract summary: We study multi-charged moments and symmetry-resolved R'enyi entropy of free compact boson for multiple disjoint intervals. R'enyi entropy is sensitive to the local conformal algebra of the theory. We numerically check our results against the tight-binding model.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study multi-charged moments and symmetry-resolved R\'enyi entropy of free compact boson for multiple disjoint intervals. The R\'enyi entropy evaluation involves computing the partition function of the theory on Riemann surfaces with genus g>1. This makes R\'enyi 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 R\'enyi entropy. The multi-charged moments are obtained by studying the correlation function of flux-generating vertex operators on the associated Riemann surface. Symmetry-resolved R\'enyi entropy is then obtained from the Fourier transforms of the charged moments. R\'enyi 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.

Related papers

• Measurement-induced transitions for interacting fermions [43.04146484262759]
  We develop a field-theoretical framework that provides a unified approach to observables characterizing entanglement and charge fluctuations. Within this framework, we derive a replicated Keldysh non-linear sigma model (NLSM) By using the renormalization-group approach for the NLSM, we determine the phase diagram and the scaling of physical observables.
  arXiv  Detail & Related papers  (2024-10-09T18:00:08Z)
• Closed-form solutions for the Salpeter equation [41.94295877935867]
  We study the propagator of the $1+1$ dimensional Salpeter Hamiltonian, describing a relativistic quantum particle with no spin. The analytical extension of the Hamiltonian in the complex plane allows us to formulate the equivalent problem, namely the B"aumer equation. This B"aumera corresponds to the Green function of a relativistic diffusion process that interpolates between Cauchy for small times and Gaussian diffusion for large times.
  arXiv  Detail & Related papers  (2024-06-26T15:52:39Z)
• Symmetry resolution of the computable cross-norm negativity of two disjoint intervals in the massless Dirac field theory [0.8309949345495992]
  entanglement in the mixed state of a quantum field theory can be described using the cross-computable norm or realignment criterion. We study its symmetry resolution for two disjoint intervals in the ground state of the massless Dirac fermion field theory. We show that, for two disjoint intervals, they correspond to the partition function of the theory on a torus with a non-contractible charged loop.
  arXiv  Detail & Related papers  (2023-12-05T17:56:48Z)
• The Tempered Hilbert Simplex Distance and Its Application To Non-linear Embeddings of TEMs [36.135201624191026]
  We introduce three different parameterizations of finite discrete TEMs via Legendre functions of the negative tempered entropy function. Similar to the Hilbert geometry, the tempered Hilbert distance is characterized as a $t$-symmetrization of the oriented tempered Funk distance.
  arXiv  Detail & Related papers  (2023-11-22T15:24:29Z)
• Entanglement R\'enyi entropy and boson-fermion duality in massless Thirring model [0.0]
  We investigate the second R'enyi entropy of two intervals in the massless Thirring model. We derive exact results on the second R'enyi entropy, and examine the dependence on the sizes of the intervals and the coupling constant of the model.
  arXiv  Detail & Related papers  (2023-09-21T08:46:34Z)
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
  We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
  arXiv  Detail & Related papers  (2023-05-11T15:57:27Z)
• Charge imbalance resolved R\'enyi negativity for free compact boson: Two disjoint interval case [0.0]
  We study the symmetry decomposition of R'enyi negativity into charge imbalance sectors for 1+1 dimensional compact boson field with a global U(1) symmetry in the ground state for the case of two disjoint intervals.
  arXiv  Detail & Related papers  (2022-10-13T05:13:41Z)
• Multi-charged moments of two intervals in conformal field theory [0.0]
  We study the multi-charged moments for two disjoint intervals in the ground state of two $1+1$ dimensional CFTs with central charge $c=1$ and global $U(1)$ symmetry.
  arXiv  Detail & Related papers  (2022-06-03T12:29:13Z)
• Symmetry-resolved entanglement in a long-range free-fermion chain [0.0]
  We study the symmetry-resolved entanglement entropy in the ground state of a fermionic chain. We find entanglement, but comparing with the short-range counterpart its breaking occurs at a different order and it does depend on the hopping amplitudes.
  arXiv  Detail & Related papers  (2022-02-11T19:38:38Z)
• R\'enyi divergence inequalities via interpolation, with applications to generalised entropic uncertainty relations [91.3755431537592]
  We investigate quantum R'enyi entropic quantities, specifically those derived from'sandwiched' divergence. We present R'enyi mutual information decomposition rules, a new approach to the R'enyi conditional entropy tripartite chain rules and a more general bipartite comparison.
  arXiv  Detail & Related papers  (2021-06-19T04:06:23Z)
• Entanglement Entropy of Non-Hermitian Free Fermions [59.54862183456067]
  We study the entanglement properties of non-Hermitian free fermionic models with translation symmetry. Our results show that the entanglement entropy has a logarithmic correction to the area law in both one-dimensional and two-dimensional systems.
  arXiv  Detail & Related papers  (2021-05-20T14:46:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.