Algebraic vortex liquid theory of a quantum antiferromagnet on the kagome lattice

TL;DR

This paper develops an effective field theory for a gapless quantum spin liquid on the kagome lattice, using vortex duality and fermionization, describing a stable QED3 phase with emergent symmetry.

Contribution

It introduces a novel field theory approach for the kagome antiferromagnet, revealing a stable gapless spin liquid described by QED3 with SU(8) symmetry.

Findings

Describes a gapless critical spin liquid phase

Calculates thermodynamic and dynamic properties from the theory

Contrasts with other models of kagome antiferromagnets

Abstract

There is growing evidence from both experiment and numerical studies that low half-odd integer quantum spins on a kagome lattice with predominant antiferromagnetic near neighbor interactions do not order magnetically or break lattice symmetries even at temperatures much lower than the exchange interaction strength. Moreover, there appear to be a plethora of low energy excitations, predominantly singlets but also spin carrying, which suggest that the putative underlying quantum spin liquid is a gapless ``critical spin liquid'' rather than a gapped spin liquid with topological order. Here, we develop an effective field theory approach for the spin-1/2 Heisenberg model with easy-plane anisotropy on the kagome lattice. By employing a vortex duality transformation, followed by a fermionization and flux-smearing, we obtain access to a gapless yet stable critical spin liquid phase, which is described by (2+1)-dimensional quantum electrodynamics (QED$_3$) with an emergent $\mathrm{SU}(8)$ flavor symmetry. The specific heat, thermal conductivity, and dynamical structure factor are extracted from the effective field theory, and contrasted with other theoretical approaches to the kagome antiferromagnet.