Gapless spin-liquid ground state in the $S = 1/2$ kagome antiferromagnet

TL;DR

This paper uses advanced tensor-network methods to demonstrate that the ground state of the $S=1/2$ kagome antiferromagnet is a gapless spin liquid, providing new insights into frustrated quantum magnetism.

Contribution

The study applies projected entangled simplex states to conclusively identify a gapless spin-liquid ground state in the kagome antiferromagnet.

Findings

Ground state is a gapless spin liquid.

Tensor-network methods reveal new insights.

Effect of second-neighbour coupling analyzed.

Abstract

Frustrated quantum magnetism has moved to the forefront of physics research, posing fundamental questions concerning quantum disordered states, entanglement, topology and the nature of the quantum wavefunction. The defining problem in the field is one of the simplest, the ground state of the nearest-neighbour $S = 1/2$ antiferromagnetic Heisenberg model on the kagome lattice, but has defied all theoretical and numerical methods employed to date. We apply the formalism of tensor-network states (TNS), specifically the method of projected entangled simplex states (PESS), whose combination of a correct accounting for multipartite entanglement and infinite system size provides qualitatively new insight. By studying the ground-state energy, the staggered magnetization we find at all finite tensor bond dimensions and the effects of a second-neighbour coupling, we demonstrate that the ground state is a gapless spin liquid. We discuss the comparison with other numerical studies and the physical interpretation of the gapless ground state.