Finite Correlation Length Scaling of Disorder Parameter at Quantum Criticality

TL;DR

This paper introduces a finite correlation length scaling theory for disorder parameters at quantum critical points, demonstrating their behavior and symmetry breaking properties using iPEPS methods.

Contribution

It proposes a new finite correlation length scaling approach for disorder parameters and validates it with iPEPS, revealing their perimeter law decay at criticality.

Findings

Disorder parameters can be efficiently evaluated using iPEPS.

At critical points, disorder parameters decay exponentially with boundary size.

The scaling theory confirms spontaneous higher-form symmetry breaking at criticality.

Abstract

The disorder parameter, defined as the expectation value of the symmetry transformation acting on a subsystem, can be used to characterize symmetric phases as an analogy to detecting spontaneous symmetry breaking (SSB) phases using local order parameters. In a dual picture, disorder parameters actually detect SSB of higher-form symmetries. In this work, we show that the non-local disorder parameters can be conveniently and efficiently evaluated using infinite projected entangled pair states (iPEPS). Moreover, we propose a finite correlation length scaling theory of the disorder parameter within the quantum critical region and validate the scaling theory with variationally optimized iPEPS. We find from the finite correlation length scaling that the disorder parameter satisfies perimeter law at a critical point, i.e., it decays exponentially with the boundary size of the subsystem, indicating spontaneous higher-form symmetry breaking at the critical point of the dual model.