SciPost Submission Page
Higgs Phases and Boundary Criticality
by Kristian Tyn Kai Chung, Rafael Flores-Calderón, Rafael C. Torres, Pedro Ribeiro, Sergej Moroz, Paul McClarty
Submission summary
| Authors (as registered SciPost users): | Kristian Chung · Sergej Moroz |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202409_00007v1 (pdf) |
| Date submitted: | 2024-09-06 17:03 |
| Submitted by: | Chung, Kristian |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approaches: | Theoretical, Computational |
Abstract
Motivated by recent work connecting Higgs phases to symmetry protected topological (SPT) phases, we investigate the interplay of gauge redundancy and global symmetry in lattice gauge theories with Higgs fields in the presence of a boundary. The core conceptual point is that a global symmetry associated to a Higgs field, which is pure-gauge in a closed system, acts physically at the boundary under boundary conditions which allow electric flux to escape the system. We demonstrate in both Abelian and non-Abelian models that this symmetry is spontaneously broken in the Higgs regime, implying the presence of gapless edge modes. Starting with the U(1) Abelian Higgs model in 4D, we demonstrate a boundary phase transition in the 3D XY universality class separating the bulk Higgs and confining regimes. Varying the boundary coupling while preserving the symmetries shifts the location of the boundary phase transition. We then consider non-Abelian gauge theories with fundamental and group-valued Higgs matter, and identify the analogous non-Abelian global symmetry acting on the boundary generated by the total color charge. For SU(N) gauge theory with fundamental Higgs matter we argue for a boundary phase transition in the O(2N) universality class, verified numerically for N=2,3. For group-valued Higgs matter, the boundary theory is a principal chiral model exhibiting chiral symmetry breaking. We further demonstrate this mechanism in theories with higher-form Higgs fields. We show how the higher-form matter symmetry acts at the boundary and can spontaneously break, exhibiting a boundary confinement-deconfinement transition. We also study the electric-magnetic dual theory, demonstrating a dual magnetic defect condensation transition at the boundary. We discuss some implications and extensions of these findings and what they may imply for the relation between Higgs and SPT phases.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Report
This work studies the phase diagram of various gauge theories, focusing in particular on a gapped-phase region which contains two qualitatively different sub-regions --- the Higgs sub-region and the confined sub-region. It is believed that there is no thermodynamic transition between these two subregions, but a phase transition can occur at the boundary of open geometries. The authors use analytical arguments and numerical evidence for the ubiquity of such a boundary phase transition in various cases: 4D U(1) theory, non-Abelian theories, and higher-form theories.
I expect this paper to be a reasonably smooth read for experts in the field, and thank the authors for being careful with their writing. I did not check the work carefully, but see no reason that the paper is wittingly incorrect. This is a solid and thorough paper, and I have only two relatively minor concerns.
1). The authors should provide a Zenodo or Github link to their numerics for others to check and learn.
2). The work could use a bit more context. In particular, the authors could expand the readership if they could link this direction to the use of boundaries in topological error-correcting codes. Could there be any important consequences of this boundary transition in general, and for quantum information processing specifically? Answering this question is not a requirement for acceptance, just something I hope the authors can think about more. I list potentially related papers, part of which discuss boundaries of various 4D Z2 theories, and none of which are required to be cited:
https://arxiv.org/abs/1805.01836
https://arxiv.org/abs/2110.14644
https://arxiv.org/abs/2111.12096
https://arxiv.org/abs/2208.07367
https://arxiv.org/abs/2310.16982
https://arxiv.org/abs/2405.11719
https://arxiv.org/abs/2407.07951
Recommendation
Publish (meets expectations and criteria for this Journal)