$J_1-J_2$ quantum Heisenberg antiferromagnet on the triangular lattice: a group symmetry analysis of order by disorder

TL;DR

This paper uses group symmetry analysis and exact spectra calculations to show how quantum fluctuations select colinear order in a frustrated quantum Heisenberg antiferromagnet on a triangular lattice.

Contribution

It provides a detailed symmetry-based analysis of quantum order selection in the $J_1$-$J_2$ Heisenberg model, clarifying the role of quantum fluctuations.

Findings

Quantum fluctuations favor colinear two-sublattice order.

Symmetry analysis explains the selection mechanism.

Exact spectra support the theoretical predictions.

Abstract

On the triangular lattice, for $J_2/J_1$ between $1/8$ and $1$, the classical Heisenberg model with first and second neighbor interactions presents four-sublattice ordered ground-states. Spin-wave calculations of Chubukov and Jolicoeur\cite{cj92} and Korshunov\cite{k93} suggest that quantum fluctuations select amongst these states a colinear two-sublattice order. From theoretical requirements, we develop the full symmetry analysis of the low lying levels of the spin-1/2 Hamiltonian in the hypotheses of either a four or a two-sublattice order. We show on the exact spectra of periodic samples ($N=12,16$ and $28$) how quantum fluctuations select the colinear order from the four-sublattice order.