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Comments on Abelian Higgs Models and Persistent Order

by Zohar Komargodski, Adar Sharon, Ryan Thorngren, Xinan Zhou

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Submission summary

As Contributors: Adar Sharon · Ryan Thorngren
Arxiv Link: (pdf)
Date accepted: 2018-12-19
Date submitted: 2018-12-11 01:00
Submitted by: Thorngren, Ryan
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
Approach: Theoretical


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.

Ontology / Topics

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Abelian symmetries Ising model Quantum field theory (QFT)

Published as SciPost Phys. 6, 003 (2019)

Submission & Refereeing History

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Resubmission 1705.04786v4 on 11 December 2018

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