Persistent Corner Spin Mode at the Quantum Critical Point of a Plaquette Heisenberg Model

TL;DR

This paper investigates the robustness of dangling spin-1/2 corner states at the quantum critical point of a higher-order topological plaquette Heisenberg model, revealing a new universality class of corner critical behavior.

Contribution

It demonstrates that the dangling corner spin-1/2 state persists at the quantum critical point, indicating a novel universality class and robustness of higher-order topological corner states.

Findings

Dangling corner spin-1/2 states persist at the quantum critical point.

A new universality class of corner critical behavior is identified.

Corner states show robustness despite bulk critical fluctuations.

Abstract

Gapless edge states are the hallmark of a large class of topological states of matter. Recently, intensive research has been devoted to understanding the physical properties of the edge states at the quantum phase transitions of the bulk topological states. A higher-order symmetry-protected topological state is realized in a plaquette Heisenberg model on the square lattice. In its disordered phase, the lattice with an open boundary hosts either dangling corner states with spin-$1/2$ degeneracy characterizing the topological phase, or nondangling corner states without degeneracy, which depends on the bond configuration near the corners. In this work, we study the critical behavior of these corner states at the quantum critical point (QCP), and find that the spin-$1/2$ corner state induces a new universality class of the corner critical behavior, which is distinct from the ordinary transition of the nondangling corners. In particular, we find that the dangling spin-$1/2$ corner state persists at the QCP despite its coupling to the critical spin fluctuations in the bulk. This shows the robustness of the corner state of the higher-order topological state.