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arXiv:1306.4123 · Journal of the Physical Society of Japan

Momentum Dependent Local-Ansatz with Hybrid Wavefunction from Weak to Strong Electron Correlations

M. Atiqur R. Patoary, Yoshiro Kakehashi

Published Jul 19, 2013• 12 citations
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Abstract

The variational theory of momentum dependent local-ansatz (MLA) has been generalized by introducing a hybrid (HB) wavefunction as a starting wavefunction, whose potential can flexibly change from the Hartree-Fock type to the alloy-analogy type by varying a weighting factor from zero to one. Numerical results based on the half-filled band Hubbard model on the hypercubic lattice in infinite dimensions show up that the new wavefunction yields the ground-state energy lower than that of the Gutzwiller wavefunction (GW) in the whole Coulomb interaction regime. Calculated double occupation number is smaller than the result of the GW in the weak Coulomb interaction regime, and remains finite in the strong regime. Furthermore, the momentum distribution shows a distinct momentum dependence, which is qualitatively different from that of the GW.

DOI
10.7566/jpsj.82.084710

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The variational theory of momentum dependent local-ansatz (MLA) has been generalized by introducing a hybrid (HB) wavefunction as a starting wavefunction, whose potential can flexibly change from the Hartree-Fock type to the alloy-analogy type by varying a weighting factor from zero to one. Numerical results based on the half-filled band Hubbard model on the hypercubic lattice in infinite dimensions show up that the new wavefunction yields the ground-state energy lower than that of the Gutzwiller wavefunction (GW) in the whole Coulomb interaction regime. Calculated double occupation number is smaller than the result of the GW in the weak Coulomb interaction regime, and remains finite in the strong regime. Furthermore, the momentum distribution shows a distinct momentum dependence, which is qualitatively different from that of the GW.
The variational theory of momentum dependent local-ansatz (MLA) has been generalized by introducing a hybrid (HB) wavefunction as a starting wavefunction, whose potential can flexibly change from the Hartree-Fock type to the alloy-analogy type by varying a weighting factor from zero to one. Numerical results based on the half-filled band Hubbard model on the hypercubic lattice in infinite dimensions show up that the new wavefunction yields the ground-state energy lower than that of the Gutzwiller wavefunction (GW) in the whole Coulomb interaction regime. Calculated double occupation number is smaller than the result of the GW in the weak Coulomb interaction regime, and remains finite in the strong regime. Furthermore, the momentum distribution shows a distinct momentum dependence, which is qualitatively different from that of the GW.
Momentum dependent local-ansatz (MLA) wavefunction describes accurately electron correlations from the weak to intermediate Coulomb interaction regimes. We point out that the MLA can describe the correlations from the weak to strong Coulomb interaction regimes by modifying the starting wavefunction from the Hartree-Fock (HF) type to an alloy-analogy (AA) type wavefunction. Numerical results based on the half-filled band Hubbard model on the hypercubic lattice in infinite dimensions show up that the new wavefunction yields the ground-state energy lower than the Gutzwiller wavefunction (GW) in the whole Coulomb interaction regime. Calculated double occupation number is smaller than the result of the GW in the metallic regime, and is finite in the insulator regime. Furthermore, the momentum distribution shows a distinct momentum-dependence in both the metallic and insulator regions, which are qualitatively different from those of the GW.
We present here the momentum dependent local-ansatz wavefunction approach (MLA) with the best choice of the self-consistent variational parameters to describe the ground-state properties of the correlated electron systems in solids. With use of the self-consistent variational scheme, we performed the numerical calculations for the half-filled band as well as non-half-filled band Hubbard model on the hypercubic lattice in infinite dimensions. The ground-state energy in the MLA is lower than those of the local-ansatz approach (LA) and the Gutzwiller approach (GA) in weak and intermediate Coulomb interaction regimes. The double occupation number is suppressed as compared with the LA. We observe the distinct momentum dependence of the momentum distribution functions which is qualitatively different from those of the LA and the GA.
Momentum dependent local-ansatz wavefunction approach (MLA) to the correlated electron systems in solids has been further developed to solve best a self-consistent equation for variational parameters at non half-filling. With use of the improved variational scheme we performed the numerical calculations for the non-half-filled band Hubbard model on the hypercubic lattice in infinite dimensions. We verified that the self-consistent scheme significantly improves the correlation energy and the momentum distribution as compared with the original scheme in the MLA. We also demonstrate that the theory improves the standard variational methods such as the Local-Ansatz approach (LA) and the Gutzwiller wavefunction approach (GA); the ground-state energy in the MLA is lower than those of the LA and the GA in the weak and intermediate Coulomb interaction regimes. The double occupation number is shown to be suppressed as compared with the LA. Calculated momentum distribution functions show a distinct momentum dependence, which is qualitatively different from those of the LA and the GA.
The wavefunction method provides us with a useful tool to describe electron correlations in solids at the ground state. In this paper we review the recent development of the momentum-dependent local ansatz (MLA) wavefunction. It is constructed by taking into account two-particle excited states projected onto the local orbitals, and the momentum-dependent amplitudes of these states are chosen as variational parameters. The MLA describes accurately correlated electron states from the weak to the intermediate Coulomb interaction regime in infinite dimensions, and works well even in the strongly correlated region by introducing a new starting wavefunction called the hybrid (HB) wavefunction. The MLA-HB is therefore shown to overcome the limitation of the original local ansatz (LA) wavefunction as well as the Gutzwiller wavefunction. In particular, the calculated quasiparticle weight versus Coulomb interaction curve is shown to be close to that obtained by the numerical renormalization group approach. It is also shown that the MLA is applicable to the first-principles Hamiltonian.
A new wavefunction which improves the Gutzwiller-type local ansatz method has been proposed to describe the correlated electron system. The ground-state energy, double occupation number, momentum distribution function, and quasiparticle weight have been calculated for the half-filled band Hubbard model in infinite dimensions. It is shown that the new wavefunction improves the local-ansatz approach (LA) proposed by Stollhoff and Fulde. Especially, calculated momentum distribution functions show a reasonable momentum dependence. The result qualitatively differs from those obtained by the LA and the Gutzwiller wavefunction. Furthermore, the present approach combined with the projection operator method CPA is shown to describe quantitatively the excitation spectra in the insulator regime as well as the critical Coulomb interactions for a gap formation in infinite dimensions.