Anomalies in the Entanglement Properties of the Square Lattice Heisenberg Model

TL;DR

This paper investigates the entanglement properties of the square-lattice Heisenberg model using various numerical methods, revealing anomalies in entanglement entropy behavior related to broken symmetry, corners, and temperature effects.

Contribution

It provides a comprehensive numerical analysis of entanglement entropy in the 2D Heisenberg model, highlighting unexpected anomalies and complex behaviors not captured by existing theories.

Findings

Area law is always satisfied.

Logarithmic terms depend on subregion size due to corners and broken symmetry.

Anomalous behavior in finite temperature mutual information as T approaches zero.

Abstract

We compute the bipartite entanglement properties of the spin-half square-lattice Heisenberg model by a variety of numerical techniques that include valence bond quantum Monte Carlo (QMC), stochastic series expansion QMC, high temperature series expansions and zero temperature coupling constant expansions around the Ising limit. We find that the area law is always satisfied, but in addition to the entanglement entropy per unit boundary length, there are other terms that depend logarithmically on the subregion size, arising from broken symmetry in the bulk and from the existence of corners at the boundary. We find that the numerical results are anomalous in several ways. First, the bulk term arising from broken symmetry deviates from an exact calculation that can be done for a mean-field Neel state. Second, the corner logs do not agree with the known results for non-interacting Boson modes. And, third, even the finite temperature mutual information shows an anomalous behavior as T goes to zero, suggesting that T->0 and L->infinity limits do not commute. These calculations show that entanglement entropy demonstrates a very rich behavior in d>1, which deserves further attention.