Constraint Effective Potential of the Staggered Magnetization in an Antiferromagnet

TL;DR

This paper uses advanced Monte Carlo methods to compute the effective potential of staggered magnetization in a quantum antiferromagnet, confirming theoretical predictions and extracting low-energy parameters.

Contribution

It introduces an improved estimator for the constraint effective potential and compares Monte Carlo results with low-energy effective field theory predictions.

Findings

Excellent agreement with magnon effective field theory

Determination of the higher-order low-energy parameter $k_0$

Validation of the universal shape of the potential

Abstract

We employ an improved estimator to calculate the constraint effective potential of the staggered magnetization in the spin $\tfrac{1}{2}$ quantum Heisenberg model using a loop-cluster algorithm. The first and second moment of the probability distribution of the staggered magnetization are in excellent agreement with the predictions of the systematic low-energy magnon effective field theory. We also compare the Monte Carlo data with the universal shape of the constraint effective potential of the staggered magnetization and study its approach to the convex effective potential in the infinite volume limit. In this way the higher-order low-energy parameter $k_0$ is determined from a fit to the numerical data.