Valence-Bond Solid phases in the spin-$1/2$ Kekule-Heisenberg model

TL;DR

This paper uses tensor network simulations to map the phase diagram of the Kekule'-Kitaev-Heisenberg model, revealing two novel valence bond solid phases with plaquette order in addition to known phases.

Contribution

It introduces a large-scale tensor network approach to identify and characterize valence bond solid phases in the Kekule'-Kitaev-Heisenberg model.

Findings

Discovery of two plaquette valence bond solid phases with symmetry preservation.

Identification of decorated plaquette ordering distinguished by a specific order parameter.

Mapping of the full ground state phase diagram including quantum spin liquid and magnetic phases.

Abstract

We map out the ground state phase diagram of the isotropic Kekule'-Kitaev model on the honeycomb lattice in the presence of the Heisenberg exchange couplings. Our study relies on large-scale tensor network simulations based on graph-based projected entangled pair state (gPEPS) approach in the thermodynamic limit. We find that on top of the quantum spin liquid (QSL) and conventional magnetically ordered phases which are typical of the Kitaev-Heisenberg model, the Kekule'-Heisenberg phase diagram, hosts two plaquette valance bond solid (VBS) phases with vanishing magnetic order. While the VBS phases preserve the symmetries of the original Hamiltonian, they differ markedly from the Kitaev spin liquid by having decorated plaquette ordering which is distinguished by a plaquette order parameter.