The Kagome Antiferromagnet: A Schwinger-Boson Mean-Field Theory Study

TL;DR

This paper investigates the quantum states of the Kagome antiferromagnet using Schwinger-boson mean-field theory, revealing different ordered and spin liquid states depending on the spin value, and aligns well with previous numerical results.

Contribution

It introduces two distinct mean-field solutions for the Kagome antiferromagnet, including a novel gapped spin liquid state for spin 1/2, and analyzes their properties.

Findings

Identifies a gapped spin liquid state for S=1/2.

Finds a conventional ordered state with q=0 for all spins.

Results agree with previous numerical calculations and thermodynamic expectations.

Abstract

The Heisenberg antiferromagnet on the Kagom\'{e} lattice is studied in the framework of Schwinger-boson mean-field theory. Two solutions with different symmetries are presented. One solution gives a conventional quantum state with $\mathbf{q}=0$ order for all spin values. Another gives a gapped spin liquid state for spin $S=1/2$ and a mixed state with both $\mathbf{q}=0$ and $\sqrt{3}\times \sqrt{3}$ orders for spin $S>1/2$. We emphasize that the mixed state exhibits two sets of peaks in the static spin structure factor. And for the case of spin $S=1/2$, the gap value we obtained is consistent with the previous numerical calculations by other means. We also discuss the thermodynamic quantities such as the specific heat and magnetic susceptibility at low temperatures and show that our result is in a good agreement with the Mermin-Wagner theorem.