Gutzwiller projected wave functions in the fermionic theory of S=1 spin chains

Abstract

We study in this paper a series of Gutzwiller projected wave functions for S=1 spin chains obtained from a fermionic mean-field theory for general S>1/2 spin systems [ Liu, Zhou and Ng Phys. Rev. B 81 224417 (2010)] applied to the bilinear-biquadratic (J-K) model. The free-fermion mean-field states before the projection are 1D paring states. By comparing the energies and correlation functions of the projected pairing states with those obtained from known results, we show that the optimized Gutzwiller projected wave functions are very good trial ground-state wave functions for the antiferromagnetic bilinear-biquadratic model in the regime K<J (−3π/4<θ<π/4). We find that different topological phases of the free-fermion paring states correspond to different spin phases: the weak pairing (topologically nontrivial) state gives rise to the Haldane phase, whereas the strong pairing (topologically trivial) state gives rise to the dimer phase. In particular, the mapping between the Haldane phase and Gutwziller wave function is exact at the Affleck-Kennedy-Lieb-Tasaki (AKLT) point K/J=1/3 [θ=tan[superscript −1](1/3)]. The transition point between the two phases determined by the optimized Gutzwiller projected wave function is in good agreement with the known result. The effect of Z[subscript 2] gauge fluctuations above the mean-field theory is analyzed.