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

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.

12 pages, 7 figures

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• On the origin of the possible chiral spin liquid state of the triangular lattice Hubbard model
• Instability of the $U(1)$ spin liquid with a large spinon Fermi surface in the Heisenberg-ring exchange model on the triangular lattice
• Dynamical spin correlations in kagome antiferromagnets: comparison of Abrikosov fermion and Schwinger boson approaches beyond mean field
• Schwinger boson theory for $S=1$ Kitaev quantum spin liquids