Entanglement and criticality in translational invariant harmonic lattice systems with finite-range interactions

Abstract

We discuss the relation between entanglement and criticality in translationally invariant harmonic lattice systems with non-randon, finite-range interactions. We show that the criticality of the system as well as validity or break-down of the entanglement area law are solely determined by the analytic properties of the spectral function of the oscillator system, which can easily be computed. In particular for finite-range couplings we find a one-to-one correspondence between an area-law scaling of the bi-partite entanglement and a finite correlation length. This relation is strict in the one-dimensional case and there is strog evidence for the multi-dimensional case. We also discuss generalizations to couplings with infinite range. Finally, to illustrate our results, a specific 1D example with nearest and next-nearest neighbor coupling is analyzed.

4 pages, one figure, revised version

References in corpus (7)

• Entanglement Entropy and Quantum Field Theory
• Entropy, entanglement, and area: analytical results for harmonic lattice systems
• Entanglement in XY Spin Chain
• Spatial structures and localization of vacuum entanglement in the linear harmonic chain
• Random Matrix Theory and Entanglement in Quantum Spin Chains
• Entanglement in spin chains and lattices with long-range Ising-type interactions
• Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory

Cited by in corpus (11)

• Statistics dependence of the entanglement entropy
• Universal behavior of the Shannon mutual information of critical quantum chains
• Entanglement dynamics in presence of diversity under decohering environments
• Distillable entanglement and area laws in spin and harmonic-oscillator systems
• Bipartite entanglement entropy of the excited states of the free fermions and the harmonic oscillators
• Violation of Entanglement-Area Law in Bosonic Systems with Bose Surfaces: Possible Application to Bose Metals
• Quantum entanglement entropy and classical mutual information in long-range harmonic oscillators
• Typical and extreme entropies of long-lived isolated quantum systems
• Quantum correlation entropy
• Evidence of quantum phase transition in real-space vacuum entanglement of higher derivative scalar quantum field theories
• Entanglement of Collectively Interacting Harmonic Chains