Scaling of the disorder operator at (3+1)D O(3) quantum criticality

Abstract

The disorder operator, as an easily measured non-local observable, displays great potential in detecting intrinsic information of field theories. It has been systematically studied in 1d and 2d quantum systems, while the knowledge of 3d is still limited. The disorder operator associated with U(1) global symmetry exhibits rich geometric dependence on the shape of the spatial region at a quantum critical point, meanwhile, (3+1)D is the upper critical dimension for O(N) criticalities, both of which pose a challenge for exploring the disorder operator in high dimensions. In this work, we investigate the scaling behaviors of disorder operators in (3+1)D O(3) models through large-scale quantum Monte Carlo simulation combined with theoretical analysis. The universal contributions, such as the current central charge, have been revealed in our calculation, which establishes a concrete link between lattice simulations and continuum field theory. This work opens new avenues for experimental and numerical exploration of universal properties at quantum critical points in (3+1)D models.