Scaling dimensions of higher-charge monopoles at deconfined critical points

TL;DR

This paper measures the scaling dimensions of higher-charge monopoles at a deconfined critical point in a classical dimer model, providing insights into the nature of phase transitions in related quantum antiferromagnets.

Contribution

It presents the first direct determination of scaling dimensions for charge 2 and 3 monopoles at the critical point of a classical dimer model.

Findings

Scaling dimension y_2 = 1.48±0.07 for charge 2 monopoles

Scaling dimension y_3 = 0.20±0.03 for charge 3 monopoles

Charge 3 monopoles indicate a first-order transition in the JQ model

Abstract

The classical cubic dimer model has a columnar ordering transition that is continuous and described by a critical Anderson--Higgs theory containing an SU(2)-symmetric complex field minimally coupled to a noncompact U(1) gauge theory. Defects in the dimer constraints correspond to monopoles of the gauge theory, with charge determined by the deviation from unity of the dimer occupancy. By introducing such defects into Monte Carlo simulations of the dimer model at its critical point, we determine the scaling dimensions $y_2 = 1.48\pm0.07$ and $y_3 = 0.20 \pm 0.03$ for the operators corresponding to defects of charge $q=2$ and $3$ respectively. These results, which constitute the first direct determination of the scaling dimensions, shed light on the deconfined critical point of spin-1/2 quantum antiferromagnets, thought to belong to the same universality class. In particular, the positive value of $y_3$ implies that the transition in the JQ model on the honeycomb lattice is of first order.