Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results

TL;DR

This paper provides extensive exact diagonalization data on ground state energies and spin gaps for kagome antiferromagnetic clusters up to 42 spins, analyzing finite-size effects and cluster geometries.

Contribution

It presents the largest-scale exact diagonalization results for kagome clusters, including detailed finite-size scaling and correlation analysis.

Findings

Ground state energies and spin gaps for clusters up to 42 spins.

Finite-size scaling reveals the influence of cluster geometry.

Short loops in the lattice significantly affect correlations.

Abstract

We present a comprehensive list of ground state energies and spin gaps of finite kagome clusters with up to 42 spins obtained using large-scale exact diagonalization techniques. This represents the current limit of this exact approach. For a fixed number of spins N we study several cluster shapes under periodic boundary conditions in both directions resulting in a toroidal geometry. The clusters are characterized by their side length and diagonal as well as the shortest "Manhattan" diameter of the torii. A finite-size scaling analysis of the ground state energy as well as the spin gap is then performed in terms of the shortest toroidal diameter as well as the shortest "Manhattan" diameter. The structure of the spin-spin correlations further supports the importance of short loops wrapping around the torii.