Semiclassical ordering in the large-N pyrochlore antiferromagnet

TL;DR

This paper investigates the semiclassical limit of a large-N generalization of the pyrochlore antiferromagnet, revealing a unique collinear ground state through Monte Carlo simulations that differs from linear spin-wave predictions.

Contribution

It introduces a new effective Hamiltonian based on loop expansions for the large-N pyrochlore antiferromagnet and identifies a unique collinear ground state.

Findings

Monte Carlo simulations find a unique collinear ground state.

The identified ground state differs from the linear spin-wave theory prediction.

The effective Hamiltonian is expressed as a series in loops on the lattice.

Abstract

We study the semiclassical limit of the $Sp(N)$ generalization of the pyrochlore lattice Heisenberg antiferromagnet by expanding about the $N \to \infty$ saddlepoint in powers of a generalized inverse spin. To leading order, we write down an effective Hamiltonian as a series in loops on the lattice. Using this as a formula for calculating the energy of any classical ground state, we perform Monte-Carlo simulations and find a unique collinear ground state. This state is not a ground state of linear spin-wave theory, and can therefore not be a physical (N=1) semiclassical ground state.