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Institute of Physics eBooks

Schwinger bosons

Antônio Sérgio Teixeira Pires

Published Apr 1, 2021• 0 citations
Publisher
DOI
10.1088/978-0-7503-3879-0ch5

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Bosons and Fermions

Arnout Jozef Ceulemans

Springer eBooks•Jan 1, 2022•1 citation
Atkins and Dobson [Proc. R. Soc. London Ser. A 321, 321 (1971)] have constructed coherent angular-momentum states using the Schwinger bosonic representation and operating the displacement (coherent) operator on both of the bosonic vacuum states. By performing a squeezing transformation on the bosonic coherent states we generalize the idea of Schwinger angular-momentum coherent (SAMC) states to Schwinger angular-momentum squeezed (SAMS) states. We show that these SAMS states, which are constructed from the bosonic squeezed coherent states, exhibit squeezing of Schwinger angular-momentum operators under a certain range of parameters. The properties of these states are studied and compared with their single-mode bosonic counterpart. Application of these states in increasing the accuracy of an interferometer is discussed.
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-12triangular lattice antiferromagnetic Heisenberg model (spin-12TLHAF). 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-12TLHAF 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.