Logarithmic divergence of the block entanglement entropy for the ferromagnetic Heisenberg model

Abstract

Recent studies have shown that logarithmic divergence of entanglement entropy as function of size of a subsystem is a signature of criticality in quantum models. We demonstrate that the ground state entanglement entropy of $n$ sites for ferromagnetic Heisenberg spin-1/2 chain of the length $L$ in a sector with fixed magnetization $y$ per site grows as $1/2{\log }_2\frac{n(L-n)}{L}C(y)$, where $C(y)=2\pi e(1/4-y^2)$

4 pages, 2 figs

References in corpus (2)

• Entanglement in quantum critical phenomena
• Universality of Entropy Scaling in 1D Gap-less Models

Cited by in corpus (68)

• Entanglement entropy and conformal field theory
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Entanglement Entropy dynamics in Heisenberg chains
• Entanglement entropy in fermionic Laughlin states
• Entanglement entropy in the Lipkin-Meshkov-Glick model
• Entanglement scaling in critical two-dimensional fermionic and bosonic systems
• Bipartite entanglement entropy in fractional quantum Hall states
• Entanglement entropy in collective models
• Entanglement of Exact Excited Eigenstates of the Hubbard Model in Arbitrary Dimension
• Entanglement spectrum of the two dimensional Bose-Hubbard model
• Entanglement spectrum of random-singlet quantum critical points
• Tripartite mutual information, entanglement, and scrambling in permutation symmetric systems with an application to quantum chaos
• Ellipses of Constant Entropy in the XY Spin Chain
• Bound states and entanglement in the excited states of quantum spin chains
• Entanglement in the XX spin chain with an energy current
• Entanglement entropy of highly degenerate states and fractal dimensions
• Entanglement in an SU(n) Valence-Bond-Solid State
• Exchange Symmetry and Multipartite Entanglement
• Entangling power of permutation invariant quantum states
• Multiparticle Entanglement in the Lipkin-Meshkov-Glick Model
• Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point
• Unusual area-law violation in random inhomogeneous systems
• Finite-size scaling of coherence and steered coherence in the Lipkin-Meshkov-Glick model
• Entanglement and Density Matrix of a Block of Spins in AKLT Model
• Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies
• Increasing entanglement through engineered disorder in the random Ising chain
• Entanglement entropy and the complex plane of replicas
• Comb entanglement in quantum spin chains
• Entanglement in Valence-Bond-Solid States
• Quantum many-body scars in spin models with multibody interactions
• Qubit Construction in 6D SCFTs
• Entanglement, fidelity, and quantum phase transition in antiferromagnetic-ferromagnetic alternating Heisenberg chain
• Finite-size scaling of the Shannon-Rényi entropy in two-dimensional systems with spontaneously broken continuous symmetry
• Universal finite-size amplitude and anomalous entanglement entropy of $z=2$ quantum Lifshitz criticalities in topological chains
• Pairing in spin chains and spinless fermions with next-nearest neighbour interactions
• Entanglement in permutation symmetric states, fractal dimensions, and geometric quantum mechanics
• Average pure-state entanglement entropy in spin systems with SU(2) symmetry
• $q$-analog qudit Dicke states
• Block Entanglement Entropy of Ground States with Long-Range Magnetic Order
• Optimal transport and von Neumann entropy in an Heisenberg XXZ chain out of equilibrium
• Entanglement entropy scaling of the XXZ chain
• Qudit Dicke state preparation
• Entanglement Entropy of Excited States in the Quantum Lifshitz Model
• Field-induced incommensurate ordering in the Heisenberg chains coupled by Ising interaction: Model for the ytterbium aluminum perovskite YbAlO${}_3$
• Entanglement structure of a quantum simulator: the two-component Bose-Hubbard model
• Spin-s Dicke states and their preparation
• Momentum-space analysis of multipartite entanglement at quantum phase transitions
• Entanglement properties and ground-state statistics of free bosons
• Dicke states as matrix product states
• Scaling of the von Neumann entropy across a finite temperature phase transition
• Structure of quantum correlations in momentum space and off diagonal long range order in eta pairing and BCS states
• Entanglement between random and clean quantum spin chains
• Exact results for the entanglement in 1D Hubbard models with spatial constraints
• Fractal dimension and the counting rule of the Goldstone modes
• Block Spin Density Matrix of the Inhomogeneous AKLT Model
• Quantum simulation of long range $XY$ quantum spin glass with strong area-law violation using trapped ions
• Energy space entanglement spectrum of pairing models with s-wave and p-wave symmetry
• Entanglement and edge effects in superpositions of many-body Fock states with spatial constraints
• Self-organization in many-body systems with short-range interactions: clustering, correlations and topology
• Systematic construction of asymptotic quantum many-body scar states and their relation to supersymmetric quantum mechanics
• Reduced density matrix and entanglement entropy of permutationally invariant quantum many-body systems
• Ab-Initio Approach to Many-Body Quantum Spin Dynamics
• Fractals and spontaneous symmetry breaking with type-B Goldstone modes: a perspective from entanglement
• Magnon-induced long-range correlations and their neutron-scattering signature in quantum magnets
• Exploring entanglement in finite-size quantum systems with degenerate ground state
• Goldstone modes and the golden spiral in the ferromagnetic spin-1 biquadratic model
• Generalized Lipkin-Meshkov-Glick models of Haldane-Shastry type
• Entanglement Entropy in Many-Fermion System