# Edge physics at the deconfined transition between a quantum spin Hall insulator and a superconductor

### Submission summary

 Authors (as Contributors): Chong Wang · Liujun Zou
Submission information
Date accepted: 2022-06-02
Date submitted: 2022-04-06 23:39
Submitted by: Zou, Liujun
Submitted to: SciPost Physics
Ontological classification
Specialties:
• Condensed Matter Physics - Theory
• High-Energy Physics - Theory
• Statistical and Soft Matter Physics
Approach: Theoretical

### Abstract

We study the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary. We calculate various edge properties in an $N\to\infty$ limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition, but only as "fractional" degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the quantum spin Hall state but with the full $SU(2)$ spin rotation symmetry, which cannot be realized if the bulk is gapped.

Published as SciPost Phys. 12, 196 (2022)

### List of changes

Along various minor changes, we have mainly revised the discussion of the boundary conditions and emergent anomalies. In particular,

1. We have removed the discussion of $\varphi$ on the boundary, and a more explicit argument for the boundary condition we take is given. We have also added an Appendix A for further discussion.

2. We have expanded the discussion of emergent anomalies, with a new Appendix B containing more details.

### Submission & Refereeing History

Resubmission scipost_202204_00010v1 on 6 April 2022
Submission 2110.08280v1 on 26 October 2021

## Reports on this Submission

### Report

The authors have addressed my questions and the paper should be published now.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -

### Report

The authors have adequately addressed my questions. I recommend the publication of this manuscript.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -