We study the azimuthal angle dependence of the energyenergy correlators
Universal features of higherform symmetries at phase transitions
We investigate the behavior of higherform symmetries at variousquantum phase transitions. We consider discrete 1form symmetries, whichcan be either part of the generalized concept βcategorical symmetryβ(labelled as \tilde{Z}_N^{(1)} Z Μ N ( 1 ) )introduced recently, or an explicit Z_N^{(1)} Z N ( 1 ) 1form symmetry. We demonstrate that for many quantum phase transitionsinvolving a Z_N^{(1)} Z N ( 1 ) or \tilde{Z}_N^{(1)} Z Μ N ( 1 ) symmetry, the following expectation value \langle \left( O_\mathcal{C}\right)^2 \rangle β¨ ( O π ) 2 β© takes the form \langle \left( \log O_\mathcal{C} \right)^2 \rangle \sim  \frac{A}{\epsilon} P + b \log P β¨ ( log O π ) 2 β© βΌ β A Ο΅ P + b log P , where O_\mathcal{C} O π is an operator defined associated with loop \mathcal{C} π (or its interior \mathcal{A} π ),which reduces to the Wilson loop operator for cases with an explicit Z_N^{(1)} Z N ( 1 ) 1form symmetry. P P is the perimeter of \mathcal{C} π ,and the b \log P b log P term arises from the sharp corners of the loop \mathcal{C} π ,which is consistent with recent numerics on a particular example. b b is a universal microscopicindependent number, which in (2+1)d ( 2 + 1 ) d is related to the universal conductivity at the quantum phasetransition. b b can be computed exactly for certain transitions using the dualitiesbetween (2+1)d ( 2 + 1 ) d conformal field theories developed in recent years. We also compute the"strange correlator" of O_\mathcal{C} O π : S_{\mathcal{C}} = \langle 0  O_\mathcal{C}  1 \rangle / \langle 0  1 \rangle S π = β¨ 0  O π  1 β© / β¨ 0  1 β© where 0\rangle  0 β© and 1\rangle  1 β© are manybody states with different topological nature.
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 Award ID(s):
 1920434
 NSFPAR ID:
 10382904
 Date Published:
 Journal Name:
 SciPost Physics
 Volume:
 11
 Issue:
 2
 ISSN:
 25424653
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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