Exact valence bond entanglement entropy and probability distribution in the XXX spin chain and the Potts model

Abstract

By relating the ground state of Temperley-Lieb hamiltonians to partition functions of 2D statistical mechanics systems on a half plane, and using a boundary Coulomb gas formalism, we obtain in closed form the valence bond entanglement entropy as well as the valence bond probability distribution in these ground states. We find in particular that for the XXX spin chain, the number N_c of valence bonds connecting a subsystem of size L to the outside goes, in the thermodynamic limit, as <N_c> = (4/pi^2) ln L, disproving a recent conjecture that this should be related with the von Neumann entropy, and thus equal to 1/(3 ln 2) ln L. Our results generalize to the Q-state Potts model.

4 pages, 2 figures

References in corpus (11)

• Entanglement Entropy and Quantum Field Theory
• Ground state overlap and quantum phase transitions
• Interacting anyons in topological quantum liquids: The golden chain
• Entanglement entropy of random quantum critical points in one dimension
• Ground state projection of quantum spin systems in the valence bond basis
• Some formal results for the valence bond basis
• Entanglement entropy at infinite randomness fixed points in higher dimensions
• Valence Bond Entanglement Entropy
• Increasing of entanglement entropy from pure to random quantum critical chains
• Entanglement entropy of the random spin-1 Heisenberg chain
• Entanglement entropy and the simulation of Quantum Mechanics

Cited by in corpus (30)

• Quantum entanglement in condensed matter systems
• Bipartite Fluctuations as a Probe of Many-Body Entanglement
• Entanglement entropy in quantum impurity systems and systems with boundaries
• Entanglement Transition in the Projective Transverse Field Ising Model
• Entanglement entropy of excited states
• Entanglement and dynamics of diffusion-annihilation processes with Majorana defects
• Entanglement Negativity at Measurement-Induced Criticality
• Bi-partite entanglement entropy in massive two-dimensional quantum field theory
• Entanglement, combinatorics and finite-size effects in spin-chains
• Logarithmic observables in critical percolation
• Valence Bond and von Neumann Entanglement Entropy in Heisenberg Ladders
• Majorana Loop Models for Measurement-Only Quantum Circuits
• Entanglement evolution across defects in critical anisotropic Heisenberg chains
• Valence bond entanglement entropy of frustrated spin chains
• Four-point geometrical correlation functions in the two-dimensional $Q$-state Potts model: connections with the RSOS models
• Hardcore dimer aspects of the SU(2) Singlet wavefunction
• Valence Bond Entanglement and Fluctuations in Random Singlet Phases
• Shared Information in Stationary States at Criticality
• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Definitions of entanglement entropy of spin systems in the valence-bond basis
• Dilute oriented loop models
• Monte Carlo Simulations of Interacting Anyon Chains
• Correlation functions in conformal invariant stochastic processes
• Entanglement entropy and localization in disordered quantum chains
• Valence bond distribution and correlation in bipartite Heisenberg antiferromagnets
• Flow to Nishimori universality in weakly monitored quantum circuits with qubit loss
• From conformal invariance to quasistationary states
• Two-point boundary correlation functions of dense loop models
• Quasi-stationary states in nonlocal stochastic growth models with infinitely many absorbing states
• Entanglement of quantum spin systems: a valence-bond approach