Critical exponents of the quantum phase transition in a planar antiferromagnet

TL;DR

This study uses large-scale quantum Monte Carlo simulations to analyze the quantum phase transition in a planar spin-1/2 Heisenberg antiferromagnet, confirming theoretical predictions about critical exponents and the irrelevance of Berry phase terms.

Contribution

It provides the first large-scale numerical verification that the critical exponents match classical 3D O(3) values, supporting the nonlinear sigma model mapping.

Findings

Dynamical exponent z=1.018±0.02

Critical exponents β, ν, η match 3D O(3) values

Berry phase terms are dangerously irrelevant

Abstract

We have performed a large scale quantum Monte Carlo study of the quantum phase transition in a planar spin-1/2 Heisenberg antiferromagnet with CaV4O9 structure. We obtain a dynamical exponent z=1.018+/-0.02. The critical exponents beta, nu and eta agree within our errors with the classical 3D O(3) exponents, expected from a mapping to the nonlinear sigma model. This confirms the conjecture of Chubukov, Sachdev and Ye [Phys. Rev. B 49, 11919 (1994)] that the Berry phase terms in the planar Heisenberg antiferromagnet are dangerously irrelevant.