Violation of Entanglement-Area Law in Bosonic Systems with Bose Surfaces: Possible Application to Bose Metals

TL;DR

This paper demonstrates that bosonic systems with Bose surfaces violate the traditional entanglement-area law, showing a logarithmic increase in entanglement entropy with subsystem size, which has implications for understanding Bose metals.

Contribution

It provides the first explicit demonstration of entanglement-area law violation in bosonic systems with Bose surfaces, using lattice models and symmetry arguments.

Findings

Entanglement entropy scales as (N^{d-1}/3)ln L for certain subsystems.

Logarithmic violation of the area law is bounded for various subsystem geometries.

Results suggest new entanglement properties in Bose metals and related systems.

Abstract

We show the violation of the entanglement-area law for bosonic systems with Bose surfaces. For bosonic systems with gapless factorized energy dispersions on a N^d Cartesian lattice in d-dimension, e.g., the exciton Bose liquid in two dimension, we explicitly show that a belt subsystem with width L preserving translational symmetry along d-1 Cartesian axes has leading entanglement entropy (N^{d-1}/3)ln L. Using this result, the strong subadditivity inequality, and lattice symmetries, we bound the entanglement entropy of a rectangular subsystem from below and above showing a logarithmic violation of the area law. For subsystems with a single flat boundary we also bound the entanglement entropy from below showing a logarithmic violation, and argue that the entanglement entropy of subsystems with arbitrary smooth boundaries are similarly bounded.