Critical behavior of the Fredenhagen-Marcu order parameter at topological phase transitions
arxiv(2024)
摘要
A nonlocal string order parameter detecting topological phase transitions has
been proposed by Fredenhagen and Marcu (FM). In this work, we find that the FM
string order parameter for the toric code in a magnetic field exhibits
universal scaling behavior near critical points by directly evaluating it in
the infinite string-length limit using infinite Projected Entangled Pair States
(iPEPS). Our results thus indicate that the FM string order parameter is a
quantitatively good order parameter to characterize topological phase
transitions. In the presence of the electric-magnetic duality symmetry, a novel
critical exponent can be extracted from the FM string order parameter, which is
consistent with the (2+1)D XY universality class. In addition, we argue that
only in the regime with emergent 1-form Wilson loop symmetry, the corresponding
FM string order parameter can faithfully detect the topological transition.
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