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 categorical symmetry (labelled as (Z) over tilde ((1))(N)) introduced recently, or an explicit Z(N)((1)) 1-form symmetry. We demonstrate that for many quantum phase transitions involving a Z(N)((1)) or (Z) over tilde ((1))(N) symmetry, the following expectation value h(logO(C))(2) i takes the form (logO(C))(2) similar to A/is an element of P + b log P, where O-C is an operator defined associated with loop C (or its interior A), which reduces to the Wilson loop operator for cases with an explicit Z(N)((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 strange correlator of O-C : S-C = < 0 vertical bar O-C vertical bar 1 >/< 0 vertical bar 1 > where vertical bar 0 > and vertical bar 1 > are many-body states with different topological nature.

Automated summary

Investigated the behavior of higher-form symmetries at various quantum phase transitions, showing that the expectation value for many transitions takes a specific form involving a universal and computable microscopic-independent b value. Calculated the strange correlator of operators associated with different topological nature states.