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arXiv:cond-mat/0304040

Generalized Schwinger boson mean field theory for two-dimensional SU(4) symmetric spin-orbital antiferromagnet

Guang-Ming Zhang

Published Apr 2, 2003• 0 citations
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Abstract

A generalized Schwinger boson representation is proposed to describe the two-dimensional SU(4) symmetric spin-orbital quantum antiferromagnet. A uniform mean field solution gives rise to an antiferromagnetic long range ordered state with a small staggered magnetization $m_{s}=0.07566$, and the recent quantum Monte Carlo simulations on rather large lattice sizes have provided strong evidence to support these mean field results.

DOI
10.48550/arxiv.cond-mat/0304040

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A generalized Schwinger boson representation is proposed to describe the two-dimensional SU(4) symmetric spin-orbital quantum antiferromagnet. A uniform mean field solution gives rise to an antiferromagnetic long range ordered state with a small staggered magnetization ms=0.07566m_{s}=0.07566ms​=0.07566, and the recent quantum Monte Carlo simulations on rather large lattice sizes have provided strong evidence to support these mean field results.
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We present the first exact results for the T=0 dynamical structure factor of finite-sized two-dimensional square-lattice spin-(1/2 antiferromagnetic Heisenberg systems with up to 16 spins. Our results are compared to a recently proposed Schwinger boson mean-field theory. We find that the mean-field theory represents an excellent approximation to the exact spin excitation spectra at all allowed wave vectors and for all system sizes studied. We also determine the mean-field value for the T=0 staggered magnetization, mMF=0.306{m}^{\mathrm{MF}=0.306}mMF=0.306, to be in excellent agreement with published Monte Carlo results.
Large-NNN SU(4) Schwinger boson theory for coupled-dimer antiferromagnets
We develop a systematic large-NNN expansion based on the Schwinger boson representation of SU(4) coherent states of dimers for the paradigmatic spin-1/21/21/2 bilayer square lattice Heisenberg antiferromagnet. This system exhibits a quantum phase transition between a quantum paramagnetic state and a Néel order state, driven by the coupling constant g=J′/Jg = J'/Jg=J′/J, which is defined as the ratio between the inter-dimer J′J'J′ and intra-dimer JJJ exchange interactions. We demonstrate that this approach accurately describes static and dynamic properties on both sides of the quantum phase transition. The critical coupling constant gc≈0.42g_c \approx 0.42gc​≈0.42 and the dynamic spin structure factor reproduce quantum Monte Carlo results with high precision. Notably, the 1/N1/N1/N corrections reveal the longitudinal mode of the magnetically ordered phase along with the overdamping caused by its decay into the two-magnon continuum. The present large-NNN SU(N)SU(N)SU(N) Schwinger boson theory can be extended to more general cases of quantum paramagnets that undergo a quantum phase transition into magnetically ordered states.
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We employ the determinant projector quantum Monte Carlo method to investigate the ground-state magnetic properties in the Mott insulating states of the half-filled SU(4)SU(4)SU(4) and SU(6)SU(6)SU(6) Fermi-Hubbard model in the two-dimensional square lattice, which is free of the sign problem. The long-range antiferromagnetic Neel order is found for the SU(4)SU(4)SU(4) case with a small residual Neel moment. Quantum fluctuations are even stronger in the SU(6)SU(6)SU(6) case. Numeric results are consistent with either a vanishing or even weaker Neel ordering than that of SU(4)SU(4)SU(4).