Rényi entanglement entropies for the compactified massless boson with open boundary conditions

Abstract

We investigate the Rényi entanglement entropies for the one-dimensional massless free boson compactified on a circle, which describes the low energy sector of several interacting many-body 1d systems (Luttinger Liquid). We focus on systems on a finite segment with open boundary conditions and possible inhomogeneities in the couplings. We provide expressions for the Rényi entropies of integer indices in terms of Fredholm determinant-like expressions. Within the homogeneous case, we reduce the problem to the solution of linear integral equations and the computation of Riemann Theta functions. We mainly focus on a single interval in the middle of the system, but results for generic bipartitions are given as well.

arXiv comment20 pages; 5 figures. Minor corrections

References in corpus (57)

• Separability Criterion for Density Matrices
• A computable measure of entanglement
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• The logarithmic negativity: A full entanglement monotone that is not convex
• On the volume of the set of mixed entangled states
• Measuring entanglement entropy through the interference of quantum many-body twins
• Quantum thermalization through entanglement in an isolated many-body system
• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Quantum entanglement in condensed matter systems
• Probing entanglement entropy via randomized measurements
• Probing entanglement in a many-body-localized system
• Entanglement negativity in quantum field theory
• Entropy scaling and simulability by Matrix Product States
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Entanglement spectrum in one-dimensional systems
• Quantum quenches in 1+1 dimensional conformal field theories
• Entanglement entropy of two disjoint intervals in conformal field theory
• Boundary conformal field theory approach to the two-dimensional critical Ising model with a defect line
• A comparison of entanglement measures
• Can One Trust Quantum Simulators?
• Entanglement negativity in extended systems: A field theoretical approach
• On the volume of the set of mixed entangled states II
• Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
• Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases
• Remarks on the entanglement entropy for disconnected regions
• Partial Teleportation of Entanglement in the Noisy Environment
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Equipartition of the Entanglement Entropy
• Maximally multipartite entangled states
• The entanglement entropy of one-dimensional gases
• Entanglement Entropy and Twist Fields
• Entanglement entropy of two disjoint blocks in critical Ising models
• Entanglement and boundary critical phenomena
• On entropy growth and the hardness of simulating time evolution
• On short interval expansion of Rényi entropy
• On Rényi entropies of disjoint intervals in conformal field theory
• On reduced density matrices for disjoint subsystems
• Emergence of curved light-cones in a class of inhomogeneous Luttinger liquids
• Entanglement entropy and negativity of disjoint intervals in CFT: Some numerical extrapolations
• Holographic Rényi entropy for CFT with $W$ symmetry
• Conformal field theory on top of a breathing one-dimensional gas of hard core bosons
• Bose-Fermi duality and entanglement entropies
• Front dynamics and entanglement in the XXZ chain with a gradient
• Spin structures and entanglement of two disjoint intervals in conformal field theories
• Entanglement entropy of two disjoint intervals and the recursion formula for conformal blocks
• Entanglement entropies of minimal models from null-vectors
• Entanglement growth and simulation efficiency in one-dimensional quantum lattice systems
• The Inhomogeneous Gaussian Free Field, with application to ground state correlations of trapped 1d Bose gases
• One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance
• Entanglement and relative entropies for low-lying excited states in inhomogeneous one-dimensional quantum systems
• New insights into the entanglement of disjoint blocks
• On one-loop entanglement entropy of two short intervals from OPE of twist operators
• Entanglement of several blocks in fermionic chains
• Probing the conformal Calabrese-Cardy scaling with cold atoms
• Entanglement, Replicas, and Thetas
• Two intervals Rényi entanglement entropy of compact free boson on torus

Cited by in corpus (9)

• Emergent conformal symmetry in non-unitary random dynamics of free fermions
• Boundary effects on symmetry resolved entanglement
• Entanglement entropies of inhomogeneous Luttinger liquids
• Multi-charged moments of two intervals in conformal field theory
• Entanglement spreading and quasiparticle picture beyond the pair structure
• Entanglement entropies of an interval for the massless scalar field in the presence of a boundary
• Holographic Entanglement Entropy of the Coulomb Branch
• Extracting the Luttinger parameter from a single wave function
• Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries