Field Theory of Quantum Antiferromagnets : From the Triangular to the Kagome Lattice

TL;DR

This paper develops a field theory framework for quantum antiferromagnets on triangular and Kagome lattices, revealing a novel phase with potential gapless excitations that preserve spin symmetry.

Contribution

It introduces a unified field theory description interpolating between the triangular and Kagome lattice antiferromagnets, identifying a new phase with unbroken spin symmetry.

Findings

Field theories for both lattice types identified

A novel phase with unbroken SO(3)_R symmetry discovered

Proposed mechanism for gapless excitations without symmetry breaking

Abstract

We analyse a family of models, that interpolates between the Triangular lattice antiferromagnet (TLAF) and the Kagome lattice antiferromagnet (KLAF). We identify the field theories governing the low energy, long wavelength physics of these models. Near the TLAF the low energy field theory is a nonlinear sigma model of a SO(3) group valued field. The SO(3) symmetry of the spin system is enhanced to a $SO(3)_R \times SO(2)_L$ symmetry in the field theory. Near the KLAF other modes become important and the field takes values in $SO(3) \times S_2$. We analyse this field theory and show that it admits a novel phase in which the $SO(3)_R$ spin symmetry is unbroken and the $SO(2)_L$ symmetry is broken. We propose this as a possible mechanism by which a gapless excitation can exist in the KLAF without breaking the spin rotation symmetry.