Entanglement Entropy of the Two-Dimensional Heisenberg Antiferromagnet

TL;DR

This paper calculates entanglement entropies in the 2D Heisenberg antiferromagnet, revealing area law behavior with logarithmic corrections, and validates results against numerical methods.

Contribution

It introduces a modified spin-wave approach with a staggered field to accurately compute entanglement entropies in the 2D Heisenberg model.

Findings

Entanglement entropies follow an area law with logarithmic corrections.

Results agree quantitatively with quantum Monte Carlo and DMRG.

Spin fluctuations exhibit a multiplicative logarithmic correction.

Abstract

We compute the von Neumann and generalized R\'{e}nyi entanglement entropies in the ground-state of the spin-1/2 antiferromagnetic Heisenberg model on the square lattice using the modified spin-wave theory for finite lattices. The addition of a staggered magnetic field to regularize the Goldstone modes associated with symmetry-breaking is shown to be essential for obtaining well-behaved values for the entanglement entropy. The von Neumann and R\'{e}nyi entropies obey an area law with additive logarithmic corrections, and are in good quantitative agreement with numerical results from valence bond quantum Monte Carlo and density matrix renormalization group calculations. We also compute the spin fluctuations and observe a multiplicative logarithmic correction to the area law in excellent agreement with quantum Monte Carlo calculations.