Bounds on the entanglement entropy of droplet states in the XXZ spin chain
arXiv:1709.10428 · doi:10.1063/1.5007035
Abstract
We consider a class of one-dimensional quantum spin systems on the finite lattice , related to the XXZ spin chain in its Ising phase. It includes in particular the so-called droplet Hamiltonian. The entanglement entropy of energetically low-lying states over a bipartition is investigated and proven to satisfy a logarithmic bound in terms of , where denotes the maximal number of down spins in the considered state. Upon addition of any (positive) random potential the bound becomes uniformly constant on average, thereby establishing an area law. The proof is based on spectral methods: a deterministic bound on the local (many-body integrated) density of states is derived from an energetically motivated Combes--Thomas estimate.
arXiv comment15 pages
References in corpus (23)
- Area laws for the entanglement entropy - a review
- Entanglement entropy and conformal field theory
- Average Entropy of a Subsystem
- Unbounded growth of entanglement in models of many-body localization
- Many body localization in Heisenberg XXZ magnet in a random field
- Phenomenology of fully many-body-localized systems
- A phenomenology of certain many-body-localized systems
- Universal slow growth of entanglement in interacting strongly disordered systems
- Entanglement entropy of fermions in any dimension and the Widom conjecture
- Violation of the entropic area law for Fermions
- A short review on entanglement in quantum spin systems
- Exponential Decay of Correlations Implies Area Law
- Criticality and entanglement in random quantum systems
- On the Area Law for Disordered Free Fermions
- A Special Case Of A Conjecture By Widom With Implications To Fermionic Entanglement Entropy
- Localization Properties of the XY Spin Chain. A review of mathematical results with an eye toward Many-Body Localization
- Low-energy Fock-space localization for attractive hard-core particles in disorder
- Large Block Properties of the Entanglement Entropy of Disordered Fermions
- Droplet States in the XXZ Heisenberg Chain
- Quasi-Adiabatic Continuation in Gapped Spin and Fermion Systems: Goldstone's Theorem and Flux Periodicity
- Entanglement Dynamics of Disordered Quantum XY Chains
- Droplet Excitations for the Spin-1/2 XXZ Chain with Kink Boundary Conditions
- Many-body localization in the droplet spectrum of the random XXZ quantum spin chain
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