Norikazu Tomita

The SDW-CDW Phase Transition in the One Dimensional Extended Hubbard Model

We study the SDW-CDW phase transition in the one dimensional extended Hubbard model at a half-filling. A scaling analysis using the resonating Hartree-Fock method with the numbers of electrons from 8 to 20 strongly suggests that the ground state is many-fold degenerate( 1 A 1 + , 1 B 1 + , 3 A 2 - , and 3 B 2 - states) in the SDW region while it is doubly degenerate( 1 A 1 + and 1 B 2 - states) in the CDW region. Only the 1 A 1 + state makes a continuous phase transition from the SDW state to the CDW one. The 1 B 1 + , 3 A 2 - , and 3 B 2 - states cross the 1 B 2 - state around the phase boundary. We show that the continuous phase transition in the 1 A 1 + state is brought about by defects connecting the SDW-CDW domains called halfons. The correlation structures of these states are shown to clarify the origin of the degeneracies of the ground states.

Ab initio molecular orbital calculations by the resonating Hartree-Fock approach: superposition of non-orthogonal Slater determinants

Abstract The resonating Hartree-Fock (ResHF) method is applied to ab initio MO calculations of CO. This method approximates correlated wavefunctions by superposition of non-orthogonal Slater determinants, where both the CI coefficients and the orbitals in the determinants are variationally determined. The ResHF, with two or three generating determinants, explains the correlation energy to the same extent as the full-valence CASSCF wavefunction with 328 CSFs. Furthermore, the method reproduces the dipole moment more accurately, reflecting a better long-range behavior of the wavefunction. This implies the ResHF method provides more suitable reference functions in multireference methods.

Resonating Hartree-Fock Studies on Electron Correlation and Bond Alternation in the One Dimensional Half Filled Hubbard Model

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.

Intermediately Correlated Many-electron Systems Studied by Quantum Monte Carlo Method

We have theoretically studied various one-dimensional half-filled Hubbard models from weak correlation cases to strong ones, and calculated the Lehmann spectra of the momentum-specified one-body Gr...

Resonating Hartree-Fock Studies on Electronic Structures of Excited States in the One Dimensional Bond Alternated Hubbard Model

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 (QFs) are two kinds of SDW neutral solitons whose centers are on a long bond and a short bond, respectively, and magnon fragments. QFs 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 QFs. The QFs 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 QFs are k -dependent and scaled density wave like oscillations. A part of the QFs looks like unscaled SDW defects.

Regular density waves in the half filled 1D extended Hubbard model with a bond alternation

Abstract We study the mean field regular density waves, SDW, CDW, BOW (bond order wave) and SBOW (spin BOW ), in the half filled 1D extended Hubbard model with a bond alternation x as a basis to understand abnormal features of SDW solitons at x ≠ 0. We obtain analytic expressions of their gap parameters and energies in the weak coupling limit. The two BOW phases degenerate at x = 0 split at x ≠ 0. We calculate the phase map of the mean field ground state, the existence domains of the SDW and CDW , and x dependences of the density waves.

Real Time Relaxation Dynamics of Macroscopically Photo-Excited Electrons toward the Fermi Degeneracy Formation in the Conduction Band of Semiconductors

Concerning with the recent experiment of time-resolved two-photon photo-emission spectral measurements on semiconductors (GaAs, InP), we theoretically study real time relaxation dynamics of macroscopically photo-excited electrons, toward the Fermi degeneracy formation in an originally vacant conduction band of these semiconductors. Very soon after the photo-excitation, the whole electrons are shown to exhibit a quite rapid relaxation, like an avalanching phenomenon, mainly due to successive multi-(optical and acoustic) phonon emission from them. Repeating this multi-phonon process, the whole energy distribution of the electrons is shown to become a multi-peaked structure largely elongated over the lower part of the wide conduction band. However, after around 1 ps from the excitation, this relaxation critically slows down, since the emission of a long-wave acoustic phonon from electrons around the Fermi level becomes prohibitively difficult. By using the electron temperature approximation, we show that this slow relaxation is inversely proportional to time. Thus, the formation of the complete Fermi degeneracy takes an infinite time. These theoretical results are quite consistent to the aforementioned recent experiment.

Anomalies in spin of SDW solitons and in charge of CDW solitons in the 1D extended Hubbard model with a bond alternation

Abstract In the 1D extended Hubbard model with a bond alternation x, mean field SDW solitons have anomalies in spin. There are two kinds of SDW neutral solitons with x dependent spins smaller than and larger than 1 2 . Their energies are different and x dependent. A SDW charged soliton has a x dependent fractional spin as well as a unit charge. There is a simple relation between spins of the neutral and charged solitons. We derive phase variable representations of the SDW solitons which lead to counting rules that explain these abnormal spins of the SDW solitons. Similar anomalies in charge occur in CDW solitons.

Elementary Defects, Halfons, Connecting the SDW and CDW in the One Dimensional Extended Hubbard Model

We show in the Hartree-Fock approximation that electronic defects which are SDW-CDW domain walls exist in the one dimensional extended Hubbard model of half filling. In the vicinity of the SDW-CDW phase boundary, SDW and CDW polarons and charged solitons split into confined pairs of these defects. They become freely mobile along a chain on the phase boundary. They have ±1/4 spins and ±1/2 charges in an equidistant lattice and are called halfons. Halfon pairs can convert smoothly the SDW and CDW and can be major quantum fluctuations in the SDW-CDW phase transition. In a bond alternated lattice their spins and charges, respectively, deviate from 1/4 and 1/2. On the SDW-CDW phase boundary, there exist new density waves called the mixed density waves (MDW). Halfons are classified by their trajectories connecting the SDW and CDW via the MDW. We derive the counting rules to explain their fractional spins and charges.

Direct determination of exciton wavefunction amplitudes by the momentum-resolved photo-electron emission experiment

We study conceptional problems of a photo-electron emission (PEE) process from a free exciton in insulating crystals. In this PEE process, only the electron constituting the exciton is suddenly emi...