Entanglement entropy of two disjoint intervals and spin structures in interacting chains in and out of equilibrium

Abstract

We take the paradigm of interacting spin chains, the Heisenberg spin-$\frac{1}{2}$ XXZ model, as a reference system and consider interacting models that are related to it by Jordan-Wigner transformations and restrictions to sub-chains. An example is the fermionic analogue of the gapless XXZ Hamiltonian, which, in a continuum scaling limit, is described by the massless Thirring model. We work out the Rényi-$\alpha$ entropies of disjoint blocks in the ground state and extract the universal scaling functions describing the Rényi-$\alpha$ tripartite information in the limit of infinite lengths. We consider also the von Neumann entropy, but only in the limit of large distance. We show how to use the entropies of spin blocks to unveil the spin structures of the underlying massless Thirring model. Finally, we speculate about the tripartite information after global quenches and conjecture its asymptotic behaviour in the limit of infinite time and small quench. The resulting conjecture for the ``residual tripartite information'', which corresponds to the limit in which the intervals' lengths are infinitely larger than their (large) distance, supports the claim of universality recently made studying noninteracting spin chains. Our mild assumptions imply that the residual tripartite information after a small quench of the anisotropy in the gapless phase of XXZ is equal to $-\log 2$.

References in corpus (69)

• A computable measure of entanglement
• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement entropy and conformal field theory
• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• The logarithmic negativity: A full entanglement monotone that is not convex
• Calculation of reduced density matrices from correlation functions
• The ITensor Software Library for Tensor Network Calculations
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Reduced density matrices and entanglement entropy in free lattice models
• Quantum Quench in the Transverse Field Ising Chain
• Generalized Gibbs ensemble in integrable lattice models
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Entanglement entropy in free quantum field theory
• Entanglement Renyi entropies in holographic theories
• Entanglement negativity in quantum field theory
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• The iTEBD algorithm beyond unitary evolution
• Susceptibility of the Spin 1/2 Heisenberg Antiferromagnetic Chain
• Entanglement entropy of two disjoint intervals in conformal field theory
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
• Form factors of branch-point twist fields in quantum integrable models and entanglement entropy
• Holographic Entanglement Entropy
• Holographic Mutual Information is Monogamous
• Scaling of entanglement support for Matrix Product States
• Entanglement and alpha entropies for a massive Dirac field in two dimensions
• Variational optimization algorithms for uniform matrix product states
• An introduction to integrable techniques for one-dimensional quantum systems
• Magnetization Plateaux in N-Leg Spin Ladders
• Remarks on the entanglement entropy for disconnected regions
• Parity effects in the scaling of block entanglement in gapless spin chains
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Reduced density matrix and internal dynamics for multicomponent regions
• Low energy effective Hamiltonian for the XXZ spin chain
• Entanglement in fermionic systems
• Entanglement Entropy and Twist Fields
• Entanglement entropy of two disjoint blocks in critical Ising models
• A Web of 2d Dualities: ${\mathbf{Z}}_2$ Gauge Fields and Arf Invariants
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Quantum phase transition between cluster and antiferromagnetic states
• On Rényi entropies of disjoint intervals in conformal field theory
• Thermalization of mutual and tripartite information in strongly coupled two dimensional conformal field theories
• Thermalization and pseudolocality in extended quantum systems
• On reduced density matrices for disjoint subsystems
• Conformal Data from Finite Entanglement Scaling
• Generalized Thirring Models
• Ellipses of Constant Entropy in the XY Spin Chain
• Entanglement Hamiltonians: from field theory, to lattice models and experiments
• Bose-Fermi duality and entanglement entropies
• Spin structures and entanglement of two disjoint intervals in conformal field theories
• A note on the Full Counting Statistics of paired fermions
• Entanglement entropy of two disjoint intervals and the recursion formula for conformal blocks
• Essential singularity in the Renyi entanglement entropy of the one-dimensional XYZ spin-1/2 chain
• Density Matrix Renormalization Group of Gapless Systems
• Topological and nematic ordered phases in many-body cluster-Ising models
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories
• Exponential decay of mutual information for Gibbs states of local Hamiltonians
• New insights into the entanglement of disjoint blocks
• The entanglement and relative entropy of a chiral fermion on the torus
• Entanglement of two disjoint intervals in conformal field theory and the 2D Coulomb gas on a lattice
• Entanglement entropy for non-coplanar regions in quantum field theory
• Entanglement, Replicas, and Thetas
• Universality in the tripartite information after global quenches
• Analytical results on the Heisenberg spin chain in a magnetic field
• Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains
• Universality in the tripartite information after global quenches: spin flip and semilocal charges

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