Valence Bond Phases in $S=1/2$ Kane-Mele-Heisenberg Model

TL;DR

This paper investigates the quantum phases of the $S=1/2$ Kane-Mele-Heisenberg model, revealing that disordered regions in the classical phase diagram correspond to ordered valence bond crystal and dimerized phases in the quantum limit.

Contribution

It introduces a comprehensive analysis of quantum valence bond phases in the KMH model using multiple computational methods, highlighting the nature of disordered regions.

Findings

Disordered classical regions become ordered quantum phases.

Identification of plaquette valence bond crystal and staggered dimerized phases.

Use of exact diagonalization and mean field theories to characterize phases.

Abstract

The phase diagram of Kane-Mele-Heisenberg (KMH) model in classical limit~\cite{zare}, contains disordered regions in the coupling space, as the result of to competition among different terms in the Hamiltonian, leading to frustration in finding a unique ground state. In this work we explore the nature of these phase in the quantum limit, for a $S=1/2$. Employing exact diagonalization (ED) in $S_z$ and nearest neighbor valence bond (NNVB) bases, bond and plaquette valence bond mean field theories, We show that the disordered regions are divided into ordered quantum states in the form of plaquette valence bond crystal(PVBC) and staggered dimerized (SD) phases.