The Quantum O(N) Heisenberg Antiferromagnet for N -> infinityy

TL;DR

This paper investigates the O(N) quantum Heisenberg antiferromagnet in the large N limit using fermionic parametrization, revealing degenerate saddle points related to dimer singlet states, with findings comparable to SU(N) models.

Contribution

It introduces a fermionic approach to analyze the O(N) quantum Heisenberg antiferromagnet at large N, highlighting degenerate saddle points and their connection to dimer singlet states.

Findings

Degenerate saddle points correspond to dimer singlet coverings.

Results align with previous SU(N) generalizations.

Large N limit simplifies the model analysis.

Abstract

We study the O(N) quantum Heisenberg antiferromagnet using a parametrisation in terms of real fermions. The N->infinity limit of the model is controlled by a saddle point that is infinitely degenerate in many cases and which represents singlet states on dimers that cover the lattice. Our results are similar to results reported previously on an SU(N) generalisation of the quantum Heisenberg antiferromagnet for N->infinity.