Comments on abelian Higgs models and persistent order

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

doi:10.21468/SciPostPhys.6.1.003

SciPost Physics

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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Submissions/Reports

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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.6.1.003
TI  - Comments on abelian Higgs models and persistent order
PY  - 2019/01/09
UR  - https://scipost.org/SciPostPhys.6.1.003
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 6
IS  - 1
SP  - 003
A1  - Komargodski, Zohar
AU  - Sharon, Adar
AU  - Thorngren, Ryan
AU  - Zhou, Xinan
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.6.1.003,
	title={{Comments on abelian Higgs models and persistent order}},
	author={Zohar Komargodski and Adar Sharon and Ryan Thorngren and Xinan Zhou},
	journal={SciPost Phys.},
	volume={6},
	pages={003},
	year={2019},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.6.1.003},
	url={https://scipost.org/10.21468/SciPostPhys.6.1.003},
}

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Ontology / Topics

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Abelian symmetries Ising model Quantum field theory (QFT)

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¹ ² Zohar Komargodski,
¹ Adar Sharon,
³ Ryan Thorngren,
² Xinan Zhou

Funders for the research work leading to this publication