On Rényi entropies of disjoint intervals in conformal field theory

Abstract

We study the Rényi entropies of N disjoint intervals in the conformal field theories given by the free compactified boson and the Ising model. They are computed as the 2N point function of twist fields, by employing the partition function of the model on a particular class of Riemann surfaces. The results are written in terms of Riemann theta functions. The prediction for the free boson in the decompactification regime is checked against exact results for the harmonic chain. For the Ising model, matrix product states computations agree with the conformal field theory result once the finite size corrections have been taken into account.

66 pages, 34 figures

References in corpus (21)

• Towards a derivation of holographic entanglement entropy
• Matrix product states represent ground states faithfully
• DMRG and periodic boundary conditions: a quantum information perspective
• Entanglement negativity in quantum field theory
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Scaling of entanglement support for Matrix Product States
• A holographic proof of the strong subadditivity of entanglement entropy
• Entanglement Entropy at Large Central Charge
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Entanglement entropy of two disjoint blocks in XY chains
• The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT
• Spatial structures and localization of vacuum entanglement in the linear harmonic chain
• Entanglement Entropy and Twist Fields
• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• Unusual Corrections to Scaling in Entanglement Entropy
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Scaling of entanglement between separated blocks in spin chains at criticality
• Universal corrections to scaling for block entanglement in spin-1/2 XX chains
• Holographic entanglement entropy for disconnected regions
• Bose-Fermi duality and entanglement entropies
• Exploiting translational invariance in Matrix Product State simulations of spin chains with periodic boundary conditions

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• Negativity spectrum of one-dimensional conformal field theories
• Symmetry resolved entanglement in integrable field theories via form factor bootstrap
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• U(1) symmetry resolved entanglement in free 1+1 dimensional field theories via form factor bootstrap
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• Entanglement entropies of minimal models from null-vectors
• Entanglement as geometry and flow
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• Relative Entanglement Entropies in 1+1-dimensional conformal field theories
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• Operator content of entanglement spectra after global quenches in the transverse field Ising chain
• Modular Hamiltonians for the massless Dirac field in the presence of a defect
• Formulas for Partial Entanglement Entropy
• Multi-charged moments of two intervals in conformal field theory
• On shape dependence of holographic entanglement entropy in AdS4/CFT3
• Improving the efficiency of variational tensor network algorithms
• Entanglement entropy from non-equilibrium Monte Carlo simulations
• Corrections to universal Rényi entropy in quasiparticle excited states of quantum chains
• Entanglement of two disjoint intervals in conformal field theory and the 2D Coulomb gas on a lattice
• Unusual Corrections to Scaling and Convergence of Universal Renyi Properties at Quantum Critical Points
• Establishing strongly-coupled 3D AdS quantum gravity with Ising dual using all-genus partition functions
• Entanglement and negativity Hamiltonians for the massless Dirac field on the half line
• Universal Rényi Entropy of Quasiparticle Excitations
• Tripartite information at long distances
• Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory -- I. Single-particle states
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• Universal entanglement and correlation measure in two-dimensional conformal field theories
• A duality principle for the multi-block entanglement entropy of free fermion systems
• Entanglement, Replicas, and Thetas
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• Probing RG flows, symmetry resolution and quench dynamics through the capacity of entanglement
• Charge imbalance resolved Rényi negativity for free compact boson: Two disjoint interval case
• Universality in the tripartite information after global quenches
• Duality transformations and the entanglement entropy of gauge theories
• Entanglement entropy of the long-range Dyson hierarchical model
• Entanglement entropies of an interval for the massless scalar field in the presence of a boundary
• Rényi entanglement entropies for the compactified massless boson with open boundary conditions
• Aspects of N-partite information in conformal field theories
• On shape dependence of holographic entanglement entropy in AdS4/CFT3 with Lifshitz scaling and hyperscaling violation
• Universality in the tripartite information after global quenches: (generalised) quantum XY models
• Loschmidt echo, emerging dual unitarity and scaling of generalized temporal entropies after quenches to the critical point
• Multi-charged moments and symmetry-resolved Rényi entropy of free compact boson for multiple disjoint intervals
• An Operator Product Expansion for the Mutual Information in AdS/CFT
• Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defects
• Replicated Entanglement Negativity for Disjoint Intervals in the Ising and Free Compact Boson Conformal Field Theories
• Rényi entropies of the massless Dirac field on the torus
• The operator algebra of cyclic orbifolds
• Universality in the tripartite information after global quenches: spin flip and semilocal charges
• Scaling of finite size effect of $\alpha$-Rényi entropy in disjointed intervals under dilation
• Entanglement entropies of an interval in the free Schrödinger field theory at finite density
• Critical exponents of block-block mutual information in one-dimensional infinite lattice systems
• Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries
• Free compact boson on branched coverings of the torus
• Entanglement entropies of an interval in the free Schrödinger field theory on the half line
• Solvable models for 2+1D quantum critical points: Loop soups of 1+1D conformal field theories
• Entanglement entropy of two disjoint intervals and spin structures in interacting chains in and out of equilibrium
• Total and Symmetry resolved Entanglement spectra in some Fermionic CFTs from the BCFT approach
• Rényi entropies for one-dimensional quantum systems with mixed boundary conditions
• A contour for the entanglement negativity of bosonic Gaussian states
• A universal approach to Renyi entropy of multiple disjoint intervals
• $2$-Rényi CCNR Negativity of Compact Boson for multiple disjoint intervals