Constraint Effective Potential of the Magnetization in the Quantum XY Model

TL;DR

This paper uses advanced Monte Carlo techniques to accurately measure the effective potential of magnetization in the quantum XY model, confirming the predictions of low-energy effective field theory with high precision.

Contribution

It provides high-precision numerical validation of the effective field theory for the quantum XY model's magnetization constraint potential.

Findings

Numerical results agree with effective field theory predictions.

Low-energy parameters determined with better than permille accuracy.

Effective theory accurately describes low-energy physics.

Abstract

Using an improved estimator in the loop-cluster algorithm, we investigate the constraint effective potential of the magnetization in the spin $\tfrac{1}{2}$ quantum XY model. The numerical results are in excellent agreement with the predictions of the corresponding low-energy effective field theory. After its low-energy parameters have been determined with better than permille precision, the effective theory makes accurate predictions for the constraint effective potential which are in excellent agreement with the Monte Carlo data. This shows that the effective theory indeed describes the physics in the low-energy regime quantitatively correctly.