Pathology of Schwinger boson mean field theory for Heisenberg spin models

TL;DR

This paper critically re-examines the Schwinger boson mean field theory for Heisenberg models, revealing it predicts incorrect phase transition orders and omits important short-range correlated phases, questioning its reliability.

Contribution

The study identifies fundamental flaws in SBMFT, including incorrect transition orders and missing phases, challenging its previous applications to cubic lattice models.

Findings

Second order transition point is a local maximum of free energy.

Mean field transitions are actually first order for certain spins.

SBMFT fails to include phases with finite short-range correlations.

Abstract

We have re-analyze the Schwinger boson mean field theory (SBMFT) for Heisenberg spin models on the cubic lattice. We find that the second order phase transition point for magnetic ordering previously reported corresponds to a local maximum of the free energy functional. For both ferromagnetic and antiferromagnetic Heisenberg models with spin $S \geq S_C$, where $S_C < 1/2$, the mean field transitions are first order from the magnetically long-ranged ordered phase to the completely uncorrelated phase. In addition to erroneously giving a first order transition for magnetic ordering, the mean field theory does not include a phase with finite short-range correlation, thus negating one of the prime advantages of SBMFT. The relevance of these pathologies to other situations beyond the cubic lattice is discussed.