Spin excitation of the Heisenberg antiferromagnet with frustration: from the bounce-lattice antiferromagnet through the maple-leaf-lattice antiferromagnet to the exact-dimer system

TL;DR

This study investigates the spin excitation gap in the frustrated Heisenberg antiferromagnet on a 2D lattice for S=1/2 and S=1, revealing gapped and gapless phases depending on interaction ratios through advanced numerical diagonalization.

Contribution

First comprehensive numerical analysis of S=1 Heisenberg antiferromagnet on this lattice, including larger clusters and new phase insights.

Findings

System is gapped for small J_d/J_b ratios.

System becomes gapless at J_d/J_b around 1.4.

For S=1, an additional gapped region exists between gapless and dimer phases.

Abstract

The spin-S Heisenberg antiferromagnet on the two-dimensional lattice is investigated for S=1/2 and S=1. We consider interaction at isolated dimers ($J_{\rm d}$) and interaction bonds that form the bounce lattice ($J_{\rm b}$). For $J_{\rm d}=J_{\rm b}$, the system is reduced to the maple-leaf-lattice antiferromagnet. We primarily conduct highly parallelized numerical diagonalization to examine the spin excitation gap above the ground state for various $J_{\rm b}/J_{\rm d}$ cases. For S=1/2, we report calculations for a 42-site cluster that has not been previously treated. The S=1 case is examined for the first time for clusters up to 24 sites. Regardless of whether S=1/2 or 1, we find that the system has a gapped nature for small $J_{\rm d}/J_{\rm b}$ and becomes gapless at $J_{\rm d}/J_{\rm b}\sim 1.4$. For S=1, we also find that another gapped region appears between the gapless case at $J_{\rm d}/J_{\rm b}\sim 1.4$ and the boundary of the exact-dimer phase.