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Comments on Abelian Higgs Models and Persistent Order

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

This Submission thread is now published as SciPost Phys. 6, 003 (2019)

Submission summary

As Contributors: Adar Sharon · Ryan Thorngren
Arxiv Link: https://arxiv.org/abs/1705.04786v4 (pdf)
Date accepted: 2018-12-19
Date submitted: 2018-12-11 01:00
Submitted by: Thorngren, Ryan
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
Approach: Theoretical

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.

Ontology / Topics

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Abelian symmetries Ising model Quantum field theory (QFT)

Published as SciPost Phys. 6, 003 (2019)



Submission & Refereeing History

Published as SciPost Phys. 6, 003 (2019)

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Resubmission 1705.04786v4 on 11 December 2018

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