Topological properties of a Valence-Bond-Solid

TL;DR

This paper uses projector quantum Monte Carlo simulations to investigate the topological characteristics of the valence-bond-solid ground state in a spin model, focusing on the winding number and domain wall energies.

Contribution

It provides a detailed analysis of the topological properties and finite-size behavior of the valence-bond-solid state in the $J$-$Q_3$ model, highlighting the role of the winding number.

Findings

Winding number is a robust topological quantum number in the thermodynamic limit.

Finite-size analysis yields domain wall energy density for the topological state.

The study confirms the topological nontrivial nature of the valence-bond-solid ground state.

Abstract

We present a projector quantum Monte Carlo study of the topological properties of the valence-bond-solid ground state in the $J$-$Q_3$ spin model on the square lattice. The winding number is a topological number counting the number of domain walls in the system and is a good quantum number in the thermodynamic limit. We study the finite-size behaviour and obtain the domain wall energy density for a topological nontrivial valence-bond-solid state.