Low-energy sector of the S=1/2 Kagome antiferromagnet

TL;DR

This paper derives an effective Hamiltonian for the S=1/2 Kagome antiferromagnet emphasizing elementary triangles, predicting an exponential increase in low-lying singlet states, a persistent singlet-triplet gap, and bound spinon states, aligning well with numerical data.

Contribution

It introduces a solvable effective Hamiltonian focusing on elementary triangles, capturing key low-energy features of the Kagome antiferromagnet.

Findings

Number of low-lying singlet states grows exponentially with system size

A finite singlet-triplet gap persists in the thermodynamic limit

Spinons form bound states with small binding energy

Abstract

Starting from a modified version of the the S=1/2 Kagome antiferromagnet to emphasize the role of elementary triangles, an effective Hamiltonian involving spin and chirality variables is derived. A mean-field decoupling that retains the quantum nature of these variables is shown to yield a Hamiltonian that can be solved exactly, leading to the following predictions: i) The number of low lying singlet states increase with the number of sites N like 1.15 to the power N; ii) A singlet-triplet gap remains in the thermodynamic limit; iii) Spinons form boundstates with a small binding energy. By comparing these properties with those of the regular Kagome lattice as revealed by numerical experiments, we argue that this description captures the essential low energy physics of that model.