Comments on abelian Higgs models and persistent order

By Z. Komargodski, Adar Sharon, Ryan Thorngren, Xinan Zhou. SciPost Physics, 2017

158 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/8e810e3c28ea8dcbb6174db40fcf38070c687b6c

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Time-reversal breaking in QCD4, walls, and dualities in 2 + 1 dimensions (2017, unknown): “(A similar analysis can be found in [8,9].”
Generalized Symmetries in Condensed Matter (2022, unknown): “Work using anomalies involving higher-form symmetries to constrain dynamics of QFT includes (150, 151, 152, 153, 154, 155, 156, 157, 158, 159) and many others.”
On 2-group global symmetries and their anomalies (2018, background): “For instance, one concrete example is U(1)ql Chern-Simons theory coupled to Nf scalars of charge q (recently discussed in [34]).”
Anomalies in the space of coupling constants and their dynamical applications II (2019, background): “Similar phenomena have been discussed in [23, 36, 38].”
Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases (2021, background): “This variation is characteristic of an anomaly associated with a d + 1-dimensional topological response ˜ A p +1 F ( B q ) [134], where ˜ A p +1 is the background p + 1-form gauge field (note the shift) associated with the center symmetry.”