Gutzwiller projected wave functions in the fermionic theory of S=1 spin chains
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 stat...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2012
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| Online Access: | http://hdl.handle.net/1721.1/73690 |
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| author | Liu, Zheng-Xin Zhou, Yi Tu, Hong-Hao Wen, Xiao-Gang Ng, Tai-Kai |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Liu, Zheng-Xin Zhou, Yi Tu, Hong-Hao Wen, Xiao-Gang Ng, Tai-Kai |
| author_sort | Liu, Zheng-Xin |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T16:05:22Z |
| format | Article |
| id | mit-1721.1/73690 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:05:22Z |
| publishDate | 2012 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/736902022-10-02T06:17:02Z Gutzwiller projected wave functions in the fermionic theory of S=1 spin chains Liu, Zheng-Xin Zhou, Yi Tu, Hong-Hao Wen, Xiao-Gang Ng, Tai-Kai Massachusetts Institute of Technology. Department of Physics Freeman, Xiao-Gang 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. Research Grants Council (Hong Kong, China) (Grant number CRF09/HKUST3) 2012-10-10T12:32:47Z 2012-10-10T12:32:47Z 2012-05 2012-05 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/73690 Liu, Zheng-Xin et al. “Gutzwiller Projected Wave Functions in the Fermionic Theory of S=1 Spin Chains.” Physical Review B 85.19 (2012). ©2012 American Physical Society en_US http://dx.doi.org/10.1103/PhysRevB.85.195144 Physical Review B Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Liu, Zheng-Xin Zhou, Yi Tu, Hong-Hao Wen, Xiao-Gang Ng, Tai-Kai Gutzwiller projected wave functions in the fermionic theory of S=1 spin chains |
| title | Gutzwiller projected wave functions in the fermionic theory of S=1 spin chains |
| title_full | Gutzwiller projected wave functions in the fermionic theory of S=1 spin chains |
| title_fullStr | Gutzwiller projected wave functions in the fermionic theory of S=1 spin chains |
| title_full_unstemmed | Gutzwiller projected wave functions in the fermionic theory of S=1 spin chains |
| title_short | Gutzwiller projected wave functions in the fermionic theory of S=1 spin chains |
| title_sort | gutzwiller projected wave functions in the fermionic theory of s 1 spin chains |
| url | http://hdl.handle.net/1721.1/73690 |
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