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Journal of Physics Conference Series

Resonating Hartree-Fock studies on magnetic states in the Hubbard model on the uniform triangular lattice

Takaaki Maruyama, Fumikazu Sato, Norikazu Tomita

Published Sep 28, 2011• 0 citations
Publisher

Abstract

We investigate the quantum fluctuations in magnetic states of the half-filled Hubbard model on the uniform triangular lattice, by means of the resonating Hartree-Fock approximation where a many-body wavefunction is constructed by non-orthogonal multi-Slater determinants. It is shown that the quantum fluctuations are described by large deviations from the 120° Neel order even at U/t = 10, which results in significant reduction of the spin correlations.

DOI
10.1088/1742-6596/320/1/012061

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We investigate the quantum fluctuations in magnetic states of the half-filled Hubbard model on the uniform triangular lattice, by means of the resonating Hartree-Fock approximation where a many-body wavefunction is constructed by non-orthogonal multi-Slater determinants. It is shown that the quantum fluctuations are described by large deviations from the 120° Neel order even at U/t = 10, which results in significant reduction of the spin correlations.
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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.
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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.
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.
Abstract We investigate magnetic correlation in the triangular lattice Hubbard model using determinant quantum Monte Carlo simulations. Focusing on the role of next-nearest-neighbor hopping t ′ and electron filling 〈 n 〉, we demonstrate that regions of high density of states, particularly near van Hove singularity (VHS) points, significantly enhance short-range ferromagnetic correlations as measured by the uniform spin susceptibility χ (Γ). Specifically, χ (Γ), quantifying ferromagnetic fluctuations, is amplified at fillings corresponding to the VHS for a given t ′ . Increasing the on-site Coulomb repulsion U further strengthens these ferromagnetic correlations, with a more pronounced effect at lower temperatures, and the observed ferromagnetic correlations are found to be short-ranged. Conversely, near half-filling 〈 n 〉 = 1.0, larger t ′ values promote antiferromagnetic (AFM) fluctuations, evidenced by an increase in χ ( K ). Our results reveal that t ′ and filling act as effective tuning parameters for manipulating the competition between ferromagnetic and AFM fluctuations in the triangular lattice.