## Comments on abelian Higgs models and persistent order

Zohar Komargodski, Adar Sharon, Ryan Thorngren, Xinan Zhou

SciPost Phys. 6, 003 (2019) · published 9 January 2019

- doi: 10.21468/SciPostPhys.6.1.003
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### Abstract

A natural question about Quantum Field Theory is whether there is a deformation to a trivial gapped phase. If the underlying theory has an anomaly, then symmetric deformations can never lead to a trivial phase. We discuss such discrete anomalies in Abelian Higgs models in 1+1 and 2+1 dimensions. We emphasize the role of charge conjugation symmetry in these anomalies; for example, we obtain nontrivial constraints on the degrees of freedom that live on a domain wall in the VBS phase of the Abelian Higgs model in 2+1 dimensions. In addition, as a byproduct of our analysis, we show that in 1+1 dimensions the Abelian Higgs model is dual to the Ising model. We also study variations of the Abelian Higgs model in 1+1 and 2+1 dimensions where there is no dynamical particle of unit charge. These models have a center symmetry and additional discrete anomalies. In the absence of a dynamical unit charge particle, the Ising transition in the 1+1 dimensional Abelian Higgs model is removed. These models without a unit charge particle exhibit a remarkably persistent order: we prove that the system cannot be disordered by either quantum or thermal fluctuations. Equivalently, when these theories are studied on a circle, no matter how small or large the circle is, the ground state is non-trivial.

### Cited by 3

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^{1 }^{2 }Zohar Komargodski, -
^{1 }Adar Sharon, -
^{3 }Ryan Thorngren, -
^{2 }Xinan Zhou

^{1}Weizmann Institute of Science^{2}Stony Brook University [SUNY Stony Brook]^{3}University of California, Berkeley [UCBL]