Competing quantum paramagnetic ground states of the Heisenberg antiferromagnet on the star lattice

TL;DR

This paper explores various quantum spin liquid and valence bond solid states in a frustrated Heisenberg antiferromagnet on the star lattice, identifying the most energetically favorable states and their stability.

Contribution

It introduces a comprehensive analysis of competing quantum ground states on the star lattice using slave particle mean field theory and energetics calculations.

Findings

A fully gapped spin liquid is the lowest energy candidate.

The spin liquid is unstable towards two distinct VBS states.

Computed triplon dispersion for VBS states and discussed experimental implications.

Abstract

We investigate various competing paramagnetic ground states of the Heisenberg antiferromagnet on the two dimensional star lattice which exhibits geometric frustration. Using slave particle mean field theory combined with a projective symmetry group analysis, we examine a variety of candidate spin liquid states on this lattice, including chiral spin liquids, spin liquids with Fermi surfaces of spinons, and nematic spin liquids which break lattice rotational symmetry. Motivated by connection to large-N SU(N) theory as well as numerical exact diagonalization studies, we also examine various valence bond solid (VBS) states on this lattice. Based on a study of energetics using Gutzwiller projected states, we find that a fully gapped spin liquid state is the lowest energy spin liquid candidate for this model. We also find, from a study of energetics using Gutzwiller projected wave functions and bond operator approaches, that this spin liquid is unstable towards two different VBS states -- a VBS state which respects all the Hamitonian symmetries and a VBS state which exhibits $\sqrt{3}\times\sqrt{3}$ order -- depending on the ratio of the Heisenberg exchange couplings on the two inequivalent bonds of the lattice. We compute the triplon dispersion in both VBS states within the bond operator approach and discuss possible implications of our work for future experiments on candidate materials.