Edge modes of topological Mott insulators and deconfined quantum critical points

TL;DR

This paper investigates the edge modes of topological Mott insulators at a deconfined quantum critical point, revealing emergent anomalies, localized edge states, and the decoupling of electronic edge modes from critical fluctuations through quantum Monte Carlo simulations.

Contribution

It demonstrates the existence of a sharp localized edge state at the DQCP and characterizes the emergent anomaly and edge electron scaling behavior in topological Mott insulators.

Findings

Edge modes are sharp and localized at the DQCP.

Bulk Goldstone modes are irrelevant at the helical Luttinger liquid fixed points.

Scaling dimension of edge electrons shows a jump at the DQCP.

Abstract

Topology and anomalies lead to edge modes that can interact with critical bulk fluctuations. To study this setup, pertaining to boundary criticality, we consider a model exhibiting a deconfined quantum critical point (DQCP) between a dynamically generated quantum spin Hall state (i.e.a topological Mott insulator) and an s-wave superconductor. For the topological Mott insulator, the bulk Goldstone modes are shown to be irrelevant at the helical Luttinger liquid fixed points. The deconfined quantum critical point is an instance of an emergent anomaly, and we observe a sharp localized edge state at this point. The sharpness of the edge mode is consistent with an ordinary phase in which electronic edge modes decouple from critical edge bosonic fluctuations. At the DQCP, the scaling dimension of the edge electron shows a jump, a feature argued to be a signature of the emergent anomaly. Our results are based on large-scale auxiliary-field quantum Monte Carlo simulations.We also carry out calculations for the Kane-Mele-Hubbard model to confirm spectral features of the ordinary and extraordinary-log phases in the vicinity of the bulk critical point.