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Chinese Journal of Physics

Pairing Correlation of the Two-dimensional Hubbard Model

Hui-Chun Chien, Y. C. Chen, Chi-Tin Shih

Published Jun 1, 2005• 2 citations
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Abstract

The d-wave pair-pair correlation of the two-dimensional Hubbard model is investigated by the power-Lanczos method. A Jastrow-BCS type wave function is used in our variational study. By assuming a monotonic behavior of the long-range pairing correlation under Lanczos iteration, we found there is no long-range pairing order in the intermediate interaction region (U ≃ 10), which is consistent with the former result by the constrained-path Monte Carlo method. We also present numerical results obtained by the exact diagonalization of the 4×4 lattice in supporting our conclusion. PACS numbers: 74.20.-z, 71.18.+y I.

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The d-wave pair-pair correlation of the two-dimensional Hubbard model is investigated by the power-Lanczos method. A Jastrow-BCS type wave function is used in our variational study. By assuming a monotonic behavior of the long-range pairing correlation under Lanczos iteration, we found there is no long-range pairing order in the intermediate interaction region (U ≃ 10), which is consistent with the former result by the constrained-path Monte Carlo method. We also present numerical results obtained by the exact diagonalization of the 4×4 lattice in supporting our conclusion. PACS numbers: 74.20.-z, 71.18.+y I.
We reported that the pair-pair correlation function of the two-dimensional t-J model does not have long-range d-wave superconducting correlations in the interesting parameter range of J/t≤0.5J/t \leq 0.5J/t≤0.5. The power-Lanczos method is used under the assumption of monotonic behavior. This assumption has been well checked in the two-dimensional t-J and attractive Hubbard model. Here we re-examine this criterion of monotonic behavior of the pairing correlation function for the one-dimensional and two-leg t-J ladder where other accurate numerical results are available. The method seems to be working well.
We present the results of a quantum Monte Carlo study of the extended sss and the ${d}_{{x}^{2}{\ensuremath{-}y}^{2}}$ pairing correlation functions for the two-dimensional Hubbard model, computed with the constrained-path Monte Carlo method. For small lattice sizes and weak interactions, we find that the ${d}_{{x}^{2}{\ensuremath{-}y}^{2}}$ pairing correlations are stronger than the extended sss pairing correlations and are positive when the pair separation exceeds several lattice constants. As the system size or the interaction strength increases, the magnitude of the long-range part of both correlation functions vanishes.
The pair-pair correlation function of the two-dimensional $t\ensuremath{-}J$ model is studied by using the power-Lanczos method under the assumption of monotonic behavior. In comparison with the results of the ideal Fermi gas, we conclude that the 2D $t\ensuremath{-}J$ model does not have long-range ddd-wave superconducting correlation in the interesting parameter range of $J/t\ensuremath{\le}0.5$. Implications of this result are also discussed.
A linked cluster expansion of the Gutzwiller variational wave function is used to study the one- and two-dimensional Hubbard model; in parallel the variational results are compared with quantum Monte Carlo simulations on finite-size lattices. Detailed results are presented for the magnetic and pairing correlations as a function of wave vector, electron density, and interaction strength U. There is no sign for superconducting long-range order although both the d-wave and the extended s-wave pairing fluctuations are substantially enhanced as U increases.
We have studied the pair susceptibilities for all possible pair wave functions that fit on a two-dimensional (2D) eight-site Hubbard cluster by exact diagonalization of the Hamiltonian. Band fillings corresponding to four and six electrons were studied (two or four holes in the half-filled band) for a wide range of Hubbard interaction strengths and temperatures. Our results show that all pairing susceptibilities are suppressed by the Hubbard repulsion. We have also carried out perturbation-theory calculations which show that the leading-order U2{U}^{2}U2 contributions to the d-wave pair susceptibility suppresses d-wave pairing over a significant temperature range. These results are consistent with recent Monte Carlo results and provide further evidence suggesting that the 2D Hubbard model does not exhibit superconductivity.
We investigate the ground-state properties of the two-dimensional Hubbard model, based on the off-diagonal wave function variational Monte Carlo method. We use an optimized wave function that is improved from an initial one-body wave function by multiplying by multiple correlation operators that are given by the form of exp(−S-S−S)-type where SSS is a suitable operator. We examine the inhomogeneous ground state at near 1/8 doping in the strongly correlated region where the on-site Coulomb interaction is larger than the bandwidth. The ddd-wave superconductivity with a spatially oscillating gap function can coexist with the charge ordering in the ground state without magnetic ordering, and superconducting condensation energy increases by this coexistence. We also show the ddd-wave pair correlation function as a function of lattice sites. The correlation function indicates that the long-range superconducting order indeed exists, and also that the strong electron correlation suppresses the pair correlation function.