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

TL;DR

This paper investigates the edge physics of a deconfined quantum phase transition between a quantum spin Hall insulator and a superconductor, revealing unique fractional edge states and universal critical behavior.

Contribution

It introduces an effective field theory for the boundary at the QSH-SC transition, highlighting the persistence of fractional edge modes and a universal fermion scaling dimension jump.

Findings

Boundary Luttinger liquid persists at transition as fractional degrees of freedom.

Physical fermion remains gapless with a universal scaling dimension jump.

Critical point acts as a gapless analogue of the QSH state with full SU(2) symmetry.

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.