The 1/N Expansion and Long Range Antiferromagnetic Order

TL;DR

This paper uses a 1/N expansion to analyze the stability of long-range antiferromagnetic order in two-dimensional Heisenberg models, providing insights into phase transitions and disordered states.

Contribution

It demonstrates that long-range order persists beyond mean field theory through all orders of 1/N, offering a new perspective on quantum antiferromagnet phases.

Findings

Long-range order survives 1/N corrections.

Cancellation of self-energy diagrams supports a Luttinger-like theorem.

Series divergences suggest routes to disordered phases.

Abstract

The staggered magnetization of the Heisenberg antiferromagnet in two dimensions can be systematically approximated by a 1/N expansion. Cancellation between self energy diagrams leads to a Luttinger-like theorem for the ground state. We prove (for a smooth enough self energy) that the long range order of mean field theory ($N$=$\infty$) survives corrections to all orders of 1/N. Divergences of this series provides a new route to the disordered phases of quantum antiferromagnets.