Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators

TL;DR

This paper introduces a method using strange correlators to detect 2D subsystem symmetry-protected topological phases, demonstrating their effectiveness through analytical construction and large-scale quantum Monte Carlo simulations.

Contribution

It provides the first unbiased large-scale quantum Monte Carlo detection method for SSPT phases using strange correlators, revealing their long-range correlations and spatial anisotropy.

Findings

Strange correlators show long-range order in SSPT phases.

Detection of topological phase transition via strange order parameters.

Observation of spatial anisotropy related to subsystem symmetries.

Abstract

We employ strange correlators to detect 2D subsystem symmetry-protected topological (SSPT) phases which are nontrivial topological phases protected by subsystem symmetries. Specifically, we analytically construct efficient strange correlators in the 2D cluster model in the presence of a uniform magnetic field and then perform the projector Quantum Monte Carlo simulation within the quantum annealing scheme. We find that strange correlators show the long-range correlation in the SSPT phase, from which we define strange order parameters to characterize the topological phase transition between the SSPT phase at low fields and the trivial paramagnetic phase at high fields. Thus, the detection of the fully localized zero modes on the 1D physical boundary of SSPT phase has been transformed into the bulk correlation measurement about the local operators with the periodic boundary condition. We also find interesting spatial anisotropy of a strange correlator, which can be intrinsically traced back to the nature of spatial anisotropy of subsystem symmetries that protect SSPT order in the 2D cluster model. By simulating strange correlators, we, therefore, provide the first unbiased large-scale quantum Monte Carlo simulation on the easy and efficient detection in the SSPT phase and open the avenue of the investigation of the subtle yet fundamental nature of the novel interacting topological phases.