Universal features of higher-form symmetries at phase transitions
We investigate the behavior of higher-form symmetries at various quantum phase transitions. We consider discrete 1-form symmetries, which can be either part of the generalized concept â€œcategorical symmetry" (labelled as Z-N(1)) introduced recently, or an explicit Z(1) 1-form symmetry. We demonstrate that for many quantum phase transitions involvN ing a ZN(1) or Z-(1) symmetry, the following expectation value ã€ˆ(log OC)2ã€‰ takes the form N ã€ˆ(log OC)2ã€‰ âˆ¼ âˆ’ AÎµ P + b log P, where OC is an operator defined associated with loop C (or its interior A), which reduces to the Wilson loop operator for cases with an explicit ZN(1) 1-form symmetry. P is the perimeter of C, and the b log P term arises from the sharp corners of the loop C, which is consistent with recent numerics on a particular example. b is a universal microscopic-independent number, which in (2 + 1)d is related to the universal conductivity at the quantum phase transition. b can be computed exactly for certain transitions using the dualities between (2 + 1)d conformal field theories developed in recent years. We also compute the â€œstrange correlator" of OC: SC = ã€ˆ0|OC|1ã€‰/ã€ˆ0|1ã€‰ where |0ã€‰ and |1ã€‰ are many-body states with different topological nature. Â© X.-C. Wu et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation.