Gapless Spin Excitations in the $S=1/2$ Kagome- and Triangular-Lattice Heisenberg Antiferromagnets

TL;DR

This study uses numerical methods to analyze $S=1/2$ kagome- and triangular-lattice Heisenberg antiferromagnets, revealing that both systems exhibit gapless spin excitations at zero magnetization.

Contribution

It provides evidence that the spin excitations are gapless in both kagome- and triangular-lattice $S=1/2$ Heisenberg antiferromagnets, using exact diagonalization and finite-size scaling.

Findings

Spin excitation is gapless in kagome-lattice antiferromagnet.

Spin excitation is gapless in triangular-lattice antiferromagnet.

Finite-size scaling supports the gapless behavior.

Abstract

The $S=1/2$ kagome- and triangular-lattice Heisenberg antiferromagnets are investigated using the numerical exact diagonalization and the finite-size scaling analysis. The behaviour of the field derivative at zero magnetization is examined for both systems. The present result indicates that the spin excitation is gapless for each system.