Gapless edge states and their stability in two-dimensional quantum magnets

TL;DR

This study uses quantum Monte Carlo simulations to investigate gapless edge states in two-dimensional quantum magnets, revealing their stability under various perturbations and their non-TL-liquid behavior, with implications for exotic magnetic phases.

Contribution

It demonstrates the existence and stability of gapless edge states in 2D spin-1/2 antiferromagnets and characterizes their non-TL-liquid nature under different perturbations.

Findings

Gapless edge modes appear in dimerized phases.

Edge state properties deviate from TL-liquid universality.

Edge states remain stable against multiple perturbations.

Abstract

We study the nature of edge states in extrinsically and spontaneously dimerized states of two-dimensional spin-1/2 antiferromagnets, by performing quantum Monte Carlo simulation. We show that a gapless edge mode emerges in the wide region of the dimerized phases, and the critical exponent of spin correlators along the edge deviates from the value of Tomonaga-Luttinger (TL) liquid universality in large but finite systems at low temperatures. We also demonstrate that the gapless nature at edges is stable against several perturbations such as external magnetic field, easy-plane XXZ anisotropy, Dzyaloshinskii-Moriya interaction, and further-neighbor exchange interactions. The edge states exhibit non TL-liquid behavior, depending strongly on model parameters and kinds of perturbations. Possible ways of detecting these edge states are discussed. Properties of edge states we show in this paper could also be used as reference points to study other edge states of more exotic gapped magnetic phases such as spin liquids.