Critical Exponents in a Quantum Phase Transition of an Anisotropic 2D Antiferromagnet

TL;DR

This paper uses advanced numerical methods to determine critical exponents in a quantum phase transition of an anisotropic 2D antiferromagnet, revealing differences from classical models and contrasting spin cases.

Contribution

It provides the first detailed calculation of critical exponents in this specific quantum phase transition using the density-matrix renormalization group method.

Findings

Exponent β matches classical Heisenberg model on the magnetic side.

Exponent zν differs from classical expectations on the disordered side.

Distinct behaviors observed between integer and half-integer spin cases.

Abstract

I use the two-step density-matrix renormalization group method to extract the critical exponents $\beta$ and $\nu$ in the transition from a N\'eel $Q=(\pi,\pi)$ phase to a magnetically disordered phase with a spin gap. I find that the exponent $\beta$ computed from the magnetic side of the transition is consistent with that of the classical Heisenberg model, but not the exponent $z\nu$ computed from the disordered side. I also show the contrast between integer and half-integer spin cases.