Anomalous quantum-critical scaling corrections in two-dimensional antiferromagnets

TL;DR

This study investigates the quantum critical behavior in two-dimensional antiferromagnets, revealing complex correction effects and identifying a new correction exponent, which challenges previous assumptions about the leading irrelevant field.

Contribution

It demonstrates the impact of cubic interactions on scaling corrections and identifies a new correction exponent, highlighting competing effects at quantum critical points.

Findings

Non-monotonic size dependence in staggered dimer model

Identification of a new correction exponent $\,\omega_2 \approx 1.25$

Large correction prefactor with a different sign from the conventional correction

Abstract

We study the N\'eel-paramagnetic quantum phase transition in two-dimensional dimerized $S=1/2$ Heisenberg antiferromagnets using finite-size scaling of quantum Monte Carlo data. We resolve the long standing issue of the role of cubic interactions arising in the bond-operator representation when the dimer pattern lacks a certain symmetry. We find non-monotonic (monotonic) size dependence in the staggered (columnar) dimerized model, where cubic interactions are (are not) present. We conclude that there is an irrelevant field in the staggered model that is not present in the columnar case, but, at variance with previous claims, it is not the leading irrelevant field. The new exponent is $\omega_2 \approx 1.25$ and the prefactor of the correction $L^{-\omega_2}$ is large and comes with a different sign from that of the formally leading conventional correction with exponent $\omega_1 \approx 0.78$. Our study highlights the possibility of competing scaling corrections at quantum critical points.