The $S=1/2$ Kagome Heisenberg Antiferromagnet Revisited

TL;DR

This study uses large-scale Lanczos diagonalization to analyze the $S=1/2$ Kagome Heisenberg antiferromagnet, revealing complex spectral structures that challenge the simple $ ext{Z}_2$ spin liquid hypothesis and suggest multiple possible ground states.

Contribution

The paper provides the largest exact diagonalization analysis of the Kagome lattice, uncovering intricate spectral features and exploring various ground state scenarios beyond the $ ext{Z}_2$ spin liquid.

Findings

Revealed complex low-energy spectral structures.

Challenged the exclusive $ ext{Z}_2$ spin liquid ground state.

Identified finite-size effects and their implications.

Abstract

We examine the perennial quantum spin-liquid candidate $S=1/2$ Heisenberg antiferromagnet on the kagome lattice. Our study is based on achieving Lanczos diagonalization of the Hamiltonian on a $48$ site cluster in sectors with dimensions as a large as $5 \times 10^{11}$. The results reveal novel intricate structures in the low-lying energy spectrum. These structures by no means unambiguously support an emerging consensus of a $\mathbb{Z}_2$ spin liquid ground state, but instead appear compatible with several scenarios, including four-fold topological degeneracy, inversion symmetry breaking and a combination thereof. We discuss finite-size effects, such as the apparent absence of ETH, and note that while considerably reduced, some are still present for the largest cluster. Finally, we observe that an XXZ model in the Ising limit reproduces remarkably well the most striking features of finite-size spectra.