Effective Hamiltonians for state selection in Heisenberg antiferromagnets

TL;DR

This paper derives effective Hamiltonians to describe how quantum fluctuations, thermal effects, and disorder select specific ground states in frustrated antiferromagnets, emphasizing the importance of biquadratic terms in simulations.

Contribution

It introduces explicit effective Hamiltonians for different selection mechanisms in frustrated antiferromagnets, including approximate forms suitable for large-$S$ classical simulations.

Findings

Effective Hamiltonians capture quantum, thermal, and disorder effects.

Biquadratic terms are crucial for modeling collinear state selection.

Approximate forms facilitate large-scale classical simulations.

Abstract

In frustrated antiferromagnets with isotropic exchange interactions, there is typically a manifold of degenerate classical ground states. This degeneracy is broken by the (free) energy of quantum or thermal fluctuations, or the uniform effects of bond disorder. We derive effective Hamiltonians to express each kind of selection effect, in both exact forms and convenient approximate forms. It is argued that biquadratic terms, representing the collinear-selecting effects of quantum fluctuations, should be included in classical simulations of large-$S$ frustrated magnets at low temperatures