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Molecular crystals and liquid crystals science technology. Section A, Molecular crystals and liquid crystals/Molecular crystals and liquid crystals science and technology. Section A, Molecular crystals and liquid crystals

Quantum Fluctuations to Destroy the Antifer-Romagnetic Spin Order in the One Dimensional Half Filled Hubbard Model

Atsushi Ikawa, Shoji Yamamoto, Hideo Fukutome

Published Sep 1, 1993• 0 citations
Publisher

Abstract

Quantum fluctuations in the one dimensional half filled Hubbard model are investigated with the resonating Hartree-Fock method with the orbital optimization. The optimized Slater determinants include an inhomo-geneous spin density wave and configurations accommodating some neutral soliton pairs. The short and long range spin orders are destroyed by quantum translational and breathing motions of soliton pairs and gapless Gaussian type fluctuations, respectively. Our calculation suggests that the lowest singlet and triplet excitation branches are the translational modes of breathing neutral soliton pairs dressed with the Gaussian type fluctuations.

DOI
10.1080/10587259308054949

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Quantum fluctuations in the one dimensional half filled Hubbard model are investigated with the resonating Hartree-Fock method with the orbital optimization. The optimized Slater determinants include an inhomo-geneous spin density wave and configurations accommodating some neutral soliton pairs. The short and long range spin orders are destroyed by quantum translational and breathing motions of soliton pairs and gapless Gaussian type fluctuations, respectively. Our calculation suggests that the lowest singlet and triplet excitation branches are the translational modes of breathing neutral soliton pairs dressed with the Gaussian type fluctuations.
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 3 B < 1 A < 1 B that are characteristic in polyenes.
The electronic structure of the one dimensional (1D) Hubbard model is calculated by the resonationg Hartree-Fock (Res HF) method. As local fluctuations in the spin density wave (SDW) in the half filled case, we consider a soliton-antisoliton pair making quantum translational and breathing motions, i.e, breathers. The breather explains 76.5% (U = 3) and 70.1% (U = 4) of the ground state correlation energy, which is better than the result of the Gutzwiller method, and gives low energy excited states with the symmetries and energetic ordering characteristic in polyenes. The fluctuations by the breather also explain the spin and density correlations.
Effects of the on-site electron-electron Coulomb interaction U on bond alternation in the one dimensional half filled Hubbard model are studied by the resonating Hartree-Fock method. Two kinds of SDW neutral solitons S 0 A and S 0 B exist in a bond alternated lattice which are centered at a long bond and a short bond, respectively. S 0 A enhances but S 0 B suppresses the alternating bond order (ABO) due to bond alternation. Quantum fluctuations in the ground state involve more S 0 A 's than S 0 B 's because the former has lower energy than the latter with increasing bond alternation so that they enhance the ABO in the true ground state and consequently the bond alternation. The spin and singlet pair correlation functions show that electrons tend to make singlet pairs on nearest neighbor short bonds even from small U 's and small bond alternations.
The electronic structure of the strongly correlated one dimensional Hubbard model is calculated by the resonating Hartree-Fock (Res HF) method. In the strong correlation regime with the Coulomb repulsion U >∼6, SDW solitons localize almost on the central two sites and only one kind of neutral soliton pair has a much smaller energy than the other pairs. As quantum fluctuations in a periodic chain with 12 sites, we consider up to three diradical breathers consisting of the low energy neutral soliton pair. The Res HF ground state can explain 77.8% ( U =6) and 80.1% ( U =8) of the exact correlation energy. This is much better than the Gutzwiller method to use the SDW as the reference state that explains about 50% of the correlation energy. The breather fluctuations explain the rapid decreases in the short distance of the spin and staggered spin correlation functions. Other correlation functions and the excited states due to the quantum fluctuations are studied.
A tractable direct optimization algorithm is developed to optimize orbitals in the Slater determinants (S-dets) in a resonating Hartree-Fock (Res HF) wave function. We reduce the variation space using the orbitals to put the first order energy variation in the steepest descent direction. The orbitals in the next iteration are determined so as to minimize the energy functional including up to the second order variation. This algorithm is applied to the one dimensional Hubbard model of half-filling. The optimized S-dets much deviate from the trial S-dets prepared from the HF calculations. The Res HF ground state generated with a few S-dets explains from 99.9 to 95.0% of the ground state correlation energy in all the correlation regimes. We have spin correlation functions with the correct short and long range behaviors and the lowest triplet and singlet spin excitations with correct dispersions, suggesting that the optimization of orbitals incorporates long range spin fluctuations and their mode-mode couplings.
Electronic structures of low lying excited states in the 1D bond alternated Hubbard model are investigated using the resonating Hartree-Fock method. In homopolar states with the wave vector k =0, main units of quantum fluctuations (QF's) are two kinds of SDW neutral solitons whose centers are on a long bond and a short bond, respectively, and magnon fragments. QF's in ionic states contain charged defects such as SDW charged solitons and polarons as well as homopolar ones. The charge, spin and singlet pair correlation functions of the excited states show different correlation structures due to different QF's. The QF's are not spatially scaled but quantum motions of defects give constant correlation energy per site. The lowest singlet and triplet collective excitations have dispersions with gaps. Their QF's are k -dependent and scaled density wave like oscillations. A part of the QF's looks like unscaled SDW defects.