Numerical-Diagonalization Study of Spin Gap Issue of the Kagome Lattice Heisenberg Antiferromagnet

TL;DR

This study uses numerical diagonalization to analyze the spin excitation gap in the kagome lattice Heisenberg antiferromagnet, revealing insights into its gapless nature through system size dependence analysis.

Contribution

It introduces a new 42-site cluster analysis and clarifies the gapless property by separately examining even and odd site systems.

Findings

No contradiction found in the gapless nature of the system.

System size dependence supports a gapless spin excitation.

New 42-site cluster results enhance understanding of kagome antiferromagnets.

Abstract

We study the system size dependence of the singlet-triplet excitation gap in the $S=1/2$ kagome-lattice Heisenberg antiferromagnet by numerical diagonalization. We successfully obtain a new result of a cluster of 42 sites. The two sequences of gaps of systems with even-number sites and that with odd-number sites are separately analyzed. Careful examination clarifies that there is no contradiction when we consider the system to be gapless.