Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains

TL;DR

This paper uncovers novel boundary phenomena and non-Landau transitions at the critical point between two symmetry-protected topological phases in spin chains, revealing rich physics of topological phase transitions.

Contribution

It demonstrates the existence of boundary symmetry-breaking phases and a boundary deconfined quantum critical point in 1D SPT phase transitions, a new phenomenon in topological matter.

Findings

Identification of stable boundary symmetry-breaking phases.

Observation of a boundary deconfined quantum critical point.

Discovery of non-Landau boundary phase transitions.

Abstract

Decades of research have revealed a deep understanding of topological quantum matter with protected edge modes. We report that even richer physics emerges when tuning between two topological phases of matter whose respective edge modes are incompatible. The frustration at the edge leads to novel boundary physics, such as symmetry-breaking phases with exotic non-Landau transitions -- even when the edge is zero-dimensional. As a minimal case study we consider spin chains with $\mathbb{Z}_3 \times \mathbb{Z}_3$ symmetry, exhibiting two nontrivial symmetry-protected topological (SPT) phases. At the bulk 1+1D critical transition between these SPT phases, we find two stable 0+1D boundary phases, each spontaneously breaking one of the $\mathbb{Z}_3$ symmetries. Furthermore, we find that a single boundary parameter tunes a non-Landau boundary critical transition between these two phases. This constitutes a 0+1D version of an exotic phenomenon driven by charged vortex condensation known as deconfined quantum criticality. This work highlights the rich unexplored physics of criticality between nontrivial topological phases and provides insights into the burgeoning field of gapless topological phases.