Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model

TL;DR

This study provides strong numerical evidence that the ground state of the $S=1/2$ kagome Heisenberg model is a gapped $Z_2$ spin liquid, challenging previous claims of valence bond crystal order.

Contribution

Using high-precision density matrix renormalization group simulations, we demonstrate that the kagome Heisenberg model's ground state is a gapped spin liquid with $Z_2$ topological order, not a valence bond crystal.

Findings

Ground state is a gapped $Z_2$ spin liquid.

Energy lower than competing valence bond crystal states.

Consistent results across multiple cylinder geometries.

Abstract

Condensed matter physicists have long sought a realistic two-dimensional (2D) magnetic system whose ground state is a {\it spin liquid}---a zero temperature state in which quantum fluctuations have melted away any form of magnetic order. The nearest-neighbor $S=1/2$ Heisenberg model on the kagome lattice has seemed an ideal candidate, but in recent years some approximate numerical approaches to it have yielded instead a valence bond crystal. We have used the density matrix renormalization group to perform very accurate simulations on numerous cylinders with circumferences up to 12 lattice spacings, finding instead of the valence bond crystal a singlet-gapped spin liquid with substantially lower energy that appears to have $Z_2$ topological order. Our results, through a combination of very low energy, short correlation lengths and corresponding small finite size effects, a new rigorous energy bound, and consistent behavior on many cylinders, provide strong evidence that the 2D ground state of this model is a gapped spin liquid.