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Progress of Theoretical Physics Supplement

Solitons and Their Dynamics in One-Dimensional SDW Systems

Akira Terai, Yoshiyuki Ono

Published Jan 1, 1993• 40 citations
Publisher

Abstract

The dynamics of solitons in spin-density-wave systems is studied numerically using the one-dimensional Hubbard model. The motion of solitons is induced by an electric field, which is introduced into the model in the form of a time-dependent vector potential. The unrestricted Hartree-Fock approximation is used. An improved method of the decomposition of exponential operator is used to solve the time-dependent Hartree-Fock equation. First, the motion of a single soliton is studied, with emphasis on discrete lattice effects. It is found that the discreteness effects reduce the soliton saturation velocity which was found in a previous paper. Second, processes of collisions between a soliton and an antisoliton are studied. The states after the collision are quite different between the cases with a charge soliton pair and with a neutral soliton pair. In the case of the charged soliton pair, the solitons repel each other and reflect to opposite directions. In the case of the neutral soliton pair. In the case of the charged soliton pair, the solitons repel each other and reflect to opposite directions. In the case of the neutral soliton pair, the solitons attract each other to make a dynamical bound state.

DOI
10.1143/ptps.113.177

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The dynamics of solitons in spin-density-wave systems is studied numerically using the one-dimensional Hubbard model. The motion of solitons is induced by an electric field, which is introduced into the model in the form of a time-dependent vector potential. The unrestricted Hartree-Fock approximation is used. An improved method of the decomposition of exponential operator is used to solve the time-dependent Hartree-Fock equation. First, the motion of a single soliton is studied, with emphasis on discrete lattice effects. It is found that the discreteness effects reduce the soliton saturation velocity which was found in a previous paper. Second, processes of collisions between a soliton and an antisoliton are studied. The states after the collision are quite different between the cases with a charge soliton pair and with a neutral soliton pair. In the case of the charged soliton pair, the solitons repel each other and reflect to opposite directions. In the case of the neutral soliton pair. In the case of the charged soliton pair, the solitons repel each other and reflect to opposite directions. In the case of the neutral soliton pair, the solitons attract each other to make a dynamical bound state.
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.
Spatially modulated magnetic phases are investigated within the mean field theory for an itinerant electron model, i.e. the Hubbard model on a two-dimensional square lattice. By numerically diagonalizing the Hamiltonian for finite-size systems under a periodic boundary condition, we examine relative stability and physical properties of several possible magnetic states. When the electron fillings are nearly half-full, the diagonally or vertically modulated spin density wave (SDW) state is stabilized over the uniform antiferromagnetic state and a crossover from the vertical to the diagonal states appears. The diagonal or vertical stripe state is characterized by the presence of the midgap band due to the soliton lattice formation inside the main SDW gap, being an insulator. The wave length λ SDW is linearly proportional to the excess carrier concentration. Excess carriers are accommodated in the form of the soliton lattice, forming a charge density wave whose wave length is λ SDW /2.
The usual mean-field description of trapped atomic Bose - Einstein condensates predicts the existence of solitons in one-dimensional and quasi-one-dimensional confinement. If the net atomic pair interaction is attractive, these solitons appear as coherently propagating matter wavepackets; if it is repulsive, soliton behaviour is seen in the motion of `holes' in the condensate density, the velocity of which is determined by the phase difference between adjoining pieces of condensate, in analogy to the familiar Josephson effect. We explore the properties of these solitons via elementary analytic models and computer simulation, and make specific suggestions for their experimental observation.
We demonstrate that the configuration interaction (CI) approximation recaptures essential features of the exact (Bethe-ansatz) solution to the one-dimensional (1D) Hubbard model. As such, it provides a valuable route for describing effects that go beyond mean-field theory for strongly correlated electron systems in higher dimensions. The CI method systematically describes fluctuation and quantum tunneling corrections to the Hartree-Fock approximation (HFA). HFA predicts that doping a half-filled Hubbard chain leads to the appearance of charged spin polarons or charged domain-wall solitons in the antiferromagnetic background. The CI method, on the other hand, describes the quantum dynamics of these charged magnetic solitons and quantum tunneling effects between various mean-field configurations. In this paper, we test the accuracy of the CI method against the exact solution of the one-dimensional Hubbard model. We find remarkable agreement between the energy of the mobile charged bosonic domain wall (as given by the CI method) and the exact energy of the doping hole (as given by the Bethe ansatz) for the entire U/tU/tU/t range. The CI method also leads to a clear demonstration of the spin-charge separation in one dimension. Addition of one doping hole to the half-filled antiferromagnetic chain results in the appearance of two different carriers: a charged bosonic domain wall (which carries the charge but no spin) and a neutral spin-1/2 domain wall (which carries the spin but no charge).
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.