Resonating Hartree-Fock Theory of the One Dimensional Hubbard Model. I. Quantum Fluctuations by SDW Solitons and Breathers

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The electronic structure of the one dimensional Hubbard model is calculated by the resonating Hartree-Fock (HF) method. Solitons in the spin density wave (SDW) order parameter (OP) make translational bands with a lot of high harmonics. Their effective masses are about 0.1 of the electron mass, so that they are potentially good charge or spin carriers. We consider diradical and zwitterionic breathers, which consist of a neutral and charged soliton-antisoliton pair, respectively, making quantum translational and breathing motions, as local quantum fluctuations in the SDW in the half filled case. The stabilization of the ground state by the resonationg breathers amounts to 76.5% (U=3) and 70.1% (U=4) of the correlation energy. This is better than the result of the Gutzwiller method. The fluctuations by breathers explain the rapid decrease of the spin correlation function in short distances and give also low energy excited states with the symmetries and energetic ordering 3B<1A<1B that are characteristic in polyenes.

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