Why the Schwinger Boson mean field theory fails to describe the spin dynamics of the triangular lattice antiferromagnetic Heisenberg model?

TL;DR

This paper critically examines the limitations of Schwinger Boson mean field theory in describing the spin dynamics of the triangular lattice antiferromagnetic Heisenberg model, highlighting its failures in capturing key excitations and proposing improvements.

Contribution

The authors identify fundamental shortcomings of SBMFT in modeling spin dynamics and introduce a generalized approach to overcome these issues.

Findings

SBMFT accurately describes the ground state but fails for dynamical properties.

SBMFT does not predict the Goldstone mode or correctly describe spin excitations.

Proposed new formalisms aim to fix these theoretical deficiencies.

Abstract

We find that the Schwinger Boson mean field theory(SBMFT) supplemented with Gutzwiller projection provides an exceedingly accurate description for the ground state of the spin-$\frac{1}{2}$ triangular lattice antiferromagnetic Heisenberg model(spin-$\frac{1}{2}$ TLHAF). However, we find the SBMFT fails even qualitatively in the description of the dynamical behavior of the system. In particular, the SBMFT fails to predict the Goldstone mode in the magnetic ordered phase. We show that the coherent peak in the two-spinon continuum in the presence of spinon condensate should not be interpreted as a magnon mode. The SBMFT also predicts incorrectly a gapless longitudinal spin fluctuation mode in the magnetic ordered phase. We show that these failures are related to the following facts: (1)Spinon condensation fails to provide a consistent description of the order parameter manifold of the 120 degree ordered phase. (2)There lacks in the SBMFT the coupling between the uncondensed spinon and the spinon condensate, which breaks both the spin rotational and the translational symmetry. (3)There lacks in the SBMFT the rigidity that is related to the no double occupancy constraint on the spinon system. We show that such failures of the SBMFT is neither restricted to the spin-$\frac{1}{2}$ TLHAF nor to the magnetic ordered phase. We proposed a generalized SBMFT to resolve the first two issues and a new formalism to address the third issue.