Bosonic Mean Field Theory of the Spiral Phases of Heisenberg Antiferromagnets on a Chain

TL;DR

This paper introduces a new bosonic mean field theory to analyze spiral phases in one-dimensional Heisenberg antiferromagnets, revealing disordered ground states, energy gaps, and exponential decay of correlations, with exactness in a large-N limit.

Contribution

A novel bosonic mean field approach for 1D Heisenberg antiferromagnets that captures spiral phases and is exact in a large-N generalization.

Findings

Disordered ground state with exponential decay of correlations.

Existence of two exponentially small energy gaps for large spin S.

Mean field theory proven exact in a large-N limit.

Abstract

We develop a novel bosonic mean field theory to describe the spiral phases of a Heisenberg antiferromagnet on a one-dimensional chain, in terms of three bosons at each site. The ground state is disordered and for large values of the spin $S$, two different and exponentially small energy gaps are found. The spin-spin correlation function is computed and is shown to decay exponentially at large distances. Our mean field theory is also shown to be exact in a large-$N$ generalization.