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Journal of the Physical Society of Japan

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

Shuji Watanabe, Masahiko Katoh, Norikazu Tomita

Published Mar 15, 2013• 0 citations
Publisher

Abstract

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.

DOI
10.7566/jpsj.82.044705

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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.
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.
Quantum fluctuations (QF's) in the two-dimensional Hubbard model are visualized by superposition of optimized nonorthogonal Slater determinants. In the half-filled system, QF's consist of rotational and translational motions of spinon-antispinon pairs, while in the lightly doped systems (delta=0.96), those motions of polarons form the QF's. It is shown that an attractive interaction works between two polarons, in the framework of a projected Hartree-Fock picture. At about 10% doping, the ground state has a stripe structure and QF's due to deviations from the uniform stripe. The present method gives the ground state energies comparable or in some cases superior to the variational Monte Carlo method with a Gutzwiller projection parameter.
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.
We develop a new general theory for large quantum fluctuations in a Fermion many-body system that cannot be described by fluctuations around the Hartree-Fock ground state but arises from resonance of different correlation structures. We start with an exact coherent state representation of a Fermion system on a unitary group. We show that the Hamiltonian in the coherent state representation has a close connection with the Hartree-Fock energy functional. From this, we can derive a new approximation called the resonating Hartree-Fock approximation in which a state is approximated by a superposition of non-orthogonal Slater determinants with different correlation structures. We derive the variation equations to determine a resonating Hartree-Fock wavefunction. We show that the resonance between degenerate broken symmetry Slater determinants may partially recover the symmetry. We discuss how to choose trial Slater determinants in a resonating Hartree-Fock wavefunction. We suggest that resonance of Slater determinats representing localized defects, such as solitons, polarons and breathers, produced in the long range order of the HF ground state may be the most important content of large quantum fluctuations in condensed matter systems.
Electronic states in the one-dimensional (1D) doped Hubbard model are described by superposition of optimized nonorthogonal Slater determinants (S-dets). Analysis on the S-dets allows us to visualize quantum fluctuations. In the weak and intermediate interaction regimes, quantum fluctuations are described by translation and breathing motions of spin-charge coupled defects called polarons as well as spin-charge decoupled defects called holons and spinons. In the strong-interaction regime, on the other hand, spin and charge fluctuations are mostly separated as spinons and holons, especially in the lightly doped systems $(\ensuremath{\delta}=0.08)$. In the highly doped systems $(\ensuremath{\delta}=0.24)$, polarons also play an important role. Finally, it is shown that in the 1/3-filled systems, the concepts of holon, spinon, and polaron do not work anymore. The electronic structure is qualitatively described by mixtures of two different density waves having triple periodicity to the lattice. The domains of these different density waves make quantum fluctuations.