Exact entanglement entropy of the XYZ model and its sine-Gordon limit

Abstract

We obtain the exact expression for the Von Neumann entropy for an infinite bipartition of the XYZ model, by connecting its reduced density matrix to the corner transfer matrix of the eight vertex model. Then we consider the anisotropic scaling limit of the XYZ chain that yields the 1+1 dimensional sine-Gordon model. We present the formula for the entanglement entropy of the latter, which has the structure of a dominant logarithmic term plus a constant, in agreement with what is generally expected for a massive quantum field theory.

13 pages, 1 figure - v2: typos corrected - v3: some references and comments of sine-Gordon result added - v4: typos corrected

References in corpus (8)

• Bi-partite entanglement entropy in massive two-dimensional quantum field theory
• Local Measures of Entanglement and Critical Exponents at Quantum Phase Transitions
• Bi-partite entanglement entropy in integrable models with backscattering
• Reflection factors and exact g-functions for purely elastic scattering theories
• Vacuum Boundary Effects
• DMRG Simulation of the SU(3) AFM Heisenberg Model
• The elliptic scattering theory of the 1/2-XYZ and higher order Deformed Virasoro Algebras
• Vacuum Structure and Boundary Renormalization Group

Cited by in corpus (36)

• Entanglement entropy and conformal field theory
• Reduced density matrices and entanglement entropy in free lattice models
• Entanglement negativity in extended systems: A field theoretical approach
• Entanglement and symmetry resolution in two dimensional free quantum field theories
• Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach
• Entanglement entropy of two disjoint intervals in c=1 theories
• The quantum sine-Gordon model with quantum circuits
• Entanglement Hamiltonians: from field theory, to lattice models and experiments
• Essential singularity in the Renyi entanglement entropy of the one-dimensional XYZ spin-1/2 chain
• Permutation operators, entanglement entropy, and the XXZ spin chain in the limit Δ-> -1
• Entanglement Content of Quantum Particle Excitations II. Disconnected Regions and Logarithmic Negativity
• Negativity spectrum in 1D gapped phases of matter
• Entanglement Content of Quantum Particle Excitations I. Free Field Theory
• Corrections to scaling for block entanglement in massive spin-chains
• Entanglement evolution across defects in critical anisotropic Heisenberg chains
• Entanglement entropy in quantum spin chains with broken reflection symmetry
• Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies
• Correlation Length and Unusual Corrections to the Entanglement Entropy
• Entanglement Entropy from Corner Transfer Matrix in Forrester Baxter non-unitary RSOS models
• Phase diagram of truncated tetrahedral model
• Massive Corrections to Entanglement in Minimal E8 Toda Field Theory
• Higher particle form factors of branch point twist fields in integrable quantum field theories
• Universal corrections to the entanglement entropy in gapped quantum spin chains: a numerical study
• Reduced density matrix and entanglement in interacting quantum field theory with Hamiltonian truncation
• Entanglement Hamiltonian in the non-Hermitian SSH model
• Modular invariance in the gapped XYZ spin 1/2 chain
• Notes on the Causal Structure in a Tensor Network
• Current mean values in the XYZ model
• Reentrant disorder-disorder transitions in generalized multicomponent Widom-Rowlinson models
• Original electric-vertex formulation of the symmetric eight-vertex model on the square lattice is fully non-universal
• Critical properties of the eight-vertex model in a field
• Quantum Correlations in Field Theory and Integrable Systems
• Exact mapping from the $(3+1)$-dimensional Skyrme model to the $(1+1)$-dimensional sine-Gordon theory and some applications
• Approaching the RSOS critical points through entanglement: one model for many universalities
• On Emergent Geometry from Entanglement Entropy in Matrix theory
• Ising ferromagnets and antiferromagnets in an imaginary magnetic field