A hidden Goldstone mechanism in the Kagom\'e lattice antiferromagnet

TL;DR

This paper investigates the phase diagram of the Heisenberg model on the Kagome lattice with competing interactions, revealing a phase with no long-range order and gapless excitations at small coupling ratios.

Contribution

It introduces a detailed analysis of the Kagome lattice antiferromagnet, identifying a novel disordered phase with unique low-energy properties.

Findings

Identification of a disordered phase with no long-range spin order

Discovery of gapless, spin-zero low-lying excitations in this phase

Phase diagram as a function of the ratio J2/J1

Abstract

In this paper, we study the phases of the Heisenberg model on the \kagome lattice with antiferromagnetic nearest neighbour coupling $J_1$ and ferromagnetic next neighbour coupling $J_2$. Analysing the long wavelength, low energy effective action that describes this model, we arrive at the phase diagram as a function of $\chi = \frac{J_2}{J_1} $. The interesting part of this phase diagram is that for small $\chi$, which includes $\chi =0$, there is a phase with no long range spin order and with gapless and spin zero low lying excitations. We discuss our results in the context of earlier, numerical and experimental work.