Spin-Peierls and spin-liquid phases of Kagomé quantum antiferromagnets

TLDR

The spin‑1/2 Kagomé Heisenberg antiferromagnet likely has a disordered ground state, invalidating conventional spin‑wave theory. The authors aim to determine the ground state using a systematic 1/n expansion with SU(n) fermions. They employ a systematic 1/n expansion of SU(n) fermions to study the ground state. The large‑n analysis reveals a dimerized phase at J̃=0 and a chiral spin‑liquid at large J̃, with a temperature‑driven transition between them and a higher‑temperature transition to a paramagnet, while finite‑n effects lift the dimer degeneracy via local resonance; the authors suggest these phases could be observed in 3He layers on graphite.

Abstract

The ground state of the spin-1/2 nearest-neighbor Heisenberg quantum antiferromagnet on the Kagomé lattice probably lacks spin order; therefore, conventional spin-wave analysis breaks down. To ascertain the ground state, we instead use a systematic 1/n expansion with SU(n) fermions. Two distinct states occur in the large-n limit, depending on the size of the biquadratic interaction J̃. When J̃=0, there are an infinite number of degenerate ground states consisting of disconnected dimers. At finite n, however, this degeneracy is broken by local resonance. In contrast, a globally resonating chiral spin-liquid phase with no spin-Peierls modulation is the likely large-n ground state at sufficiently large J̃. For intermediate values of J̃, a phase transition from the dimer state to the chiral phase occurs as the temperature increases. At a higher temperature, there is a second transition to a paramagnetic state. We comment on the possibility that these phases are experimentally realized by the nuclear magnetic moments of a second layer of 3He atoms lying on a graphite surface.