Finite Correlation Length Scaling of Disorder Parameter at Quantum Criticality

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 phases using local order parameters. In a dual picture, disorder parameters actually detect spontaneous symmetry breaking of higher-form symmetries. In this Letter, we show that the nonlocal disorder parameters can be conveniently and efficiently evaluated using infinite projected entangled pair states. 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 infinite projected entangled pair states. 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.