Nonperturbative Renormalization of the Heisenberg Spin-1/2 Antiferromagnet on the Square Lattice

TL;DR

This paper explores the critical scaling of a spin-1/2 antiferromagnet on a square lattice using nonperturbative methods, analyzing entanglement entropy near quantum critical points and comparing results with conformal field theory predictions.

Contribution

It introduces a nonperturbative approach to analyze entanglement entropy in the XXZ model, providing insights into quantum critical behavior beyond perturbative techniques.

Findings

Entanglement entropy scales according to conformal field theory near critical points.

Measurements at different anisotropies reveal quantum phase transitions.

Results support theoretical predictions for area law scaling in 2D quantum systems.

Abstract

We investigate the critical scaling of the spin-1/2 antiferromagnet on the square lattice in the easy-plane (XXZ) regime, via numerical measurements of the entanglement entropy constructed from the zeroes of a polynomial ring. We relate these results to conformal field theory predictions for the area law scaling of entanglement entropyin the vicinity of quantum critical points in gapless conformally invariant 2d quantum systems, and in gapless systems with finite Fermi surfaces. Our measurements are focused in three low-temperature regions at fixed XXZ anisotropies of $\Delta=1.01$, $\Delta=1.78$ and $\Delta=2.0$ which probe the quantum regime between the N\'eel point and Ising phase.