Physics of low energy singlet states of the Kagome lattice quantum Heisenberg antiferromagnet

TL;DR

This study investigates the low energy singlet states in the Kagome lattice quantum Heisenberg antiferromagnet by mapping to a frustrated Ising model, revealing potential ground state phases with specific dimer orderings.

Contribution

It introduces an approximate mapping to a frustrated transverse field Ising model to analyze singlet excitations and proposes candidate ground states with large unit cell dimer order.

Findings

Identification of at least two phases in the Ising model

Proposal of a ground state with large unit cell dimer order

Comparison with numerical results supports the proposed phases

Abstract

This paper is concerned with physics of the low energy singlet excitations found to exist below the spin gap in numerical studies of the Kagome lattice quantum Heisenberg antiferromagnet. Insight into the nature of these excitations is obtained by exploiting an approximate mapping to a fully frustrated transverse field Ising model on the dual dice lattice. This Ising model is shown to possess at least two phases - an ordered phase that also breaks translational symmetry with a large unit cell, and a paramagnetic phase. The former is argued to be a likely candidate for the ground state of the original Kagome magnet which thereby exhibits a specific pattern of dimer ordering with a large unit cell. Comparisons with available numerical results are made.