Nonlocal operators on the lattice for the Higgs-confinement phase transition

This is a proceedings contribution for the presentation at XQCD 2025 based on our recent paper. We study the formulation of non-local operators on the lattice for analyzing the Higgs-confinement phase transition in a gauge-Higgs model. Since the Higgs and confined phase share the same symmetries, they cannot be distinguished by local order parameters, and one needs to use the expectation value of non-local operators. In this proceedings contribution, based on our recent work, we present lattice formulations and numerical results for three non-local operators: the Polyakov loop, the ’t Hooft loop, and the Aharonov-Bohm phase. As a testing ground, we employ the charge-2 Abelian Higgs model, whose phase diagram is well established. Our simulations reproduce the known phase structure and successfully demonstrate our lattice formulation.