Resonating Hartree-Fock Method Research Articles

Nonadiabatic quantum fluctuations in the neutral ground state of tetrathiafulvalene- p -chloranil

A nonadiabatic resonating Hartree-Fock method is applied to the one-dimensional extended Hubbard model with a staggered site-diagonal potential and Su-Schrieffer-Heeger-type electron-phonon coupling to clarify the lattice and electronic structures in the charge-density-wave (CDW) ground state. It is shown that small spin-Peierls-type domains and large dimerized CDW domains appear in the main CDW state having an equidistant lattice. Interference of breathing and translational motions of these domains constitutes quantum fluctuations. The natures of different domains are analyzed by L\owdin-Feshbach partitioning method. The present results, indicating the domains in the CDW ground state as quantum fluctuations, are consistent with the experimentally observed THz electric-field-induced changes in the electronic dipole moment in the neutral phase of tetrathiafulvalene-$p$-chloranil (TTF-CA).

Resonating Hartree–Fock Studies on the Electronic Structures of the Two-Dimensional Hole-Doped Hubbard Model

Electronic structures of the two-dimensional doped Hubbard model are investigated by using the resonating Hartree–Fock method. It is shown that doped holes form polarons in a wide range of doping regions relevant to superconductivity. The momentum distribution of electrons and the spin correlation function indicate that carriers change from polarons to conventional holes as we enhance hole doping. We will visualize quantum fluctuations in these electronic states by analyzing the structures of the Slater determinants generating the resonating Hartree–Fock wave functions.

Visualization of quantum electronic and lattice fluctuations by using the resonating Hartree-Fock method

Large quantum fluctuations in the strongly correlated electron systems as well as electron-phonon coupled systems are visualized by the resonating Hartree-Fock (HF) method). We show that, in the two-dimensional Hubbard model, doped holes form topological defects called polarons. It is also shown that the quantum fluctuations drastically change the lattice structures in the Su-Schrieffer-Heeger model.

Group-theoretical and resonating Hartree-Fock studies for spin fluctuations in two-dimensional Hubbard model on triangular lattice

Magnetic structures of the two-dimensional Hubbard model on a uniform triangular lattice are investigated from the viewpoint of quantum fluctuations. First, possible spin density wave (SDW) solutions in the unrestricted Hartree-Fock approximation are group theoretically classified for the ordering vectors of ${\mathbf{Q}}_{1}=({\mathbf{G}}_{a}+{\mathbf{G}}_{b})/4$, ${\mathbf{Q}}_{2}={C}_{3}^{+}{\mathbf{Q}}_{1}$, and ${\mathbf{Q}}_{3}={C}_{3}^{\ensuremath{-}}{\mathbf{Q}}_{1}$. Then, to include the electron correlation effects efficiently, we apply the resonating Hartree-Fock method. It is shown that the spin fluctuations in the metallic ground state at $U/t\ensuremath{\sim}4.5$ are reasonably described as hybridization of two different SDW states obtained by the group theoretical classification and their low-energy excited states. These fluctuations make the long-range magnetic order significantly reduced in the correlated ground state.

Visualization of Quantum Fluctuations by Resonating Hartree-Fock Method(Current Topics)

Visualization of Quantum Fluctuations by Resonating Hartree-Fock Method(Current Topics)

Visualization of electronic structures in the two-dimensional Hubbard model—Spinons, polarons, and stripes

Quantum fluctuations (QFs) in the two-dimensional Hubbard model are visualized by using a resonating Hartree-Fock method. Wave functions of optimized multi-Slater determinants show that QFs in the half-filled system are described by vibration, translation, and rotation of spinon-antispinon pairs, while those motions of polarons constitute dominant QFs in the lightly doped systems. We show that an attractive interaction works between two polarons in the framework of a projected Hartree-Fock approximation. The ground states at about 10% doping have a stripe structure and Q’s due to deviations from a uniform stripe.

Many-body wave functions approximated by the superposition of spin-projected nonorthogonal Slater determinants in the resonating Hartree-Fock method

A resonating Hartree-Fock (Res-HF) method is revisited and improved by the complete spin projection for the interacting Fermion system. This method approximates a many-body wave function by the superposition of nonorthogonal Slater determinants (S-dets). The nonorthogonality of the S-dets makes it possible to describe the large quantum fluctuations efficiently, since each S-det naturally includes the full-electron-excitation effects from other S-dets. The molecular orbitals in every S-det, as well as the superposition coefficients, are variationally determined. So far, however, the spin contamination, caused by the conventional half-projection, has been a serious obstacle to obtain the accurate wave functions for large-size fermion systems, especially in the intermediate and large correlation regimes. In this paper, we apply the complete spin projection method to the Res-HF calculations. As an example, the improved Res-HF method is applied to the one-dimensional Hubbard model. It will be shown that the complete spin projection improves the Res-HF wave functions significantly. In fact, the correlation energies explained by the improved Res-HF method are better than those by the variational Monte Carlo method in all the correlation regimes. The correlation structures at arbitrary fillings are also well described by the improved Res-HF method.

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.

The SDW-CDW phase transition and quantum fluctuations in the one dimensional extended Hubbard model

We study the natures of the SDW-CDW phase transition and quantum fluctuations in the one dimensional extended Hubbard model using the resonating Hartree-Fock method. The size dependences of the energies of the lowest 1 A 1 +, 1 B 1 + and 1 B 2 − states suggest that the 1 A 1 + and 1 B 1 + states are degenerate in the SDW region while the 1 A 1 + and 1 B 2 − states are degenerate in the CDW region. The 1 B 1 + and 1 B 2 − states cross at the phase boundary. We show that the dominant quantum fluctuations near the phase boundary are the SDW-CDW domain walls called halfons.

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 (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.

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.

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

Quantum fluctuations in the one dimensional half filled Hubbard model are investigated with the resonating Hartree-Fock method with the orbital optimisation. The optimised Slater determinants include an inhomogenous 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