We reexamine whether the essence of high-Tc superconductivity is contained in doped Hubbard models on the square lattice by using recently developed pre-projected Gaussian-basis Monte Carlo method. The superconducting correlations of the dx2-y2 wave symmetry in the ground state at distance r decays essentially as inverse cubic of r. The upper bound of the correlation at long distances estimated by this unbiased method is 0.001, indicating that recent extensions of dynamical mean-field theories and variational methods yielded at least an order of magnitude overestimates of it. The correlations are too weak for the realistic account of the cuprate high-Tc superconductivity.
We reexamine whether the essence of high-Tc superconductivity is contained in doped Hubbard models on the square lattice by using recently developed pre-projected Gaussian-basis Monte Carlo method. The superconducting correlations of the dx2-y2 wave symmetry in the ground state at distance r decays essentially as inverse cubic of r. The upper bound of the correlation at long distances estimated by this unbiased method is 0.001, indicating that recent extensions of dynamical mean-field theories and variational methods yielded at least an order of magnitude overestimates of it. The correlations are too weak for the realistic account of the cuprate high-Tc superconductivity.
With high-Tc cuprates in mind, properties of correlated dx2-y2-wave superconducting (SC) and antiferromagnetic (AF) states are studied for the Hubbard (t-t'-U) model on square lattices, using a variational Monte Carlo method. We employ simple trial wave functions including only crucial parameters, such as a doublon-holon binding factor indispensable to describe correlated SC and normal states as doped Mott insulators. U/t, t'/t and δ(doping rate) dependence of relevant quantities are systematically calculated. As U/t increases, a sharp crossover of SC properties occurs at U_co/t \sim 10 from a conventional BCS type to a kinetic-energy-driven type for any t'/t. As δdecreases, U_co/t is smoothly connected to the Mott transition point at half filling. For U/t\lsim 5, steady superconductivity corresponding to the cuprates is not found, whereas the d-wave SC correlation function Pd^\infty rapidly increases for U/t\gsim 6 and becomes maximum at U=U_co. Comparing the δdependence of Pd^\infty with experimentally observed dome-shaped Tc and condensation energy, we find that the effective value of U for the cuprates should be larger than the band width, for which the t-J model is valid. Analyzing the kinetic energy, we reveal that for U>U_co only doped holes (electrons) become charge carriers, which will make a small Fermi surface (hole pocket), but for UU_co is determined by two factors, i.e., the AF spin correlation, which creates singlet pairs (pseudogap), and the charge mobility dominated by Mott physics.
The possibility of superconductivity in the ground state of the two-dimensional Hubbard model was investigated by means of the variational Monte Carlo method. With slight hole doping on the 6 ×6 and 10 ×10 lattices, a clear minimum was obtained on the curve of the total energy versus the amplitude of the d -wave gap function for large on-site Coulomb energies. Superconducting pair correlations were observed to be well developed. The-next-nearest-neighbor transfer was found to appreciably affect the minimum depth.
The doped Hubbard model is a simple model for high-Tc cuprate superconductors, while its ground state remains a challenge. Here, by performing state-of-the-art variational Monte Carlo calculations for the strong-coupling Hubbard model, we find evidence that the d-wave superconducting phase emerges always near the phase separation region and the superconducting order has one-to-one correspondence with the enhancement of charge compressibility. The order as well as the phase separation are vulnerable to realistic intersite Coulomb interaction, while the superexchange interaction enhances both. An appropriate combination of these two widens the stable superconducting phase.
We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors has been extensively studied on the basis of various electronic models and also electron-phonon models. In this study, we investigate the properties of superconductivity in correlated-electron systems by using numerical methods such as the variational Monte Carlo method and the quantum Monte Carlomethod. The Hubbard model is one of basic models for strongly correlated electron systems, and is regarded as the model of cuprate high temperature superconductors. The d-p model is more realistic model for cuprates. The superconducting condensation energy obtained by adopting the Gutzwiller ansatz is in reasonable agreement with the condensation energy estimated for YBa2Cu3O7. We show the phase diagram of the ground state using this method. We have further investigated the stability of striped and checkerboard states in the under-doped region. Holes doped in a half-filled square lattice lead to an incommensurate spin and charge density wave. The relationship of the hole density x and incommensurability δ, δ~x, is satisfied in the lower doping region, as indicated by the variationalMonte Carlocalculations for the two-dimensional Hubbard model. A checkerboard-like charge-density modulation with a roughly period has also been observed by scanning tunneling microscopy experiments in Bi2212 and Na-CCOC compounds. We have performed a variational Monte Carlo simulation on a two-dimensional t-t′-t″- U Hubbard model with a Bi-2212 type band structure and found that the period checkerboard spin modulation, that is characterized by multi Q vectors, is indeed stabilized. We have further performed an investigation by using a quantumMonte Carlomethod, which is a numerical method that can be used to simulate the behavior of correlated electron systems. We present a new algorithm of the quantum Monte Carlo diagonalization that is a method for the evaluation of expectation value without the negative sign problem. We compute pair correlation functions and show that pair correlation is indeed enhanced with hole doping.
In order to study the material dependence of the correlation between stripes and dx2-y2-wave superconductivity (SC) among cuprate superconductors, we have performed a variational Monte Carlo simulation on a two-dimensional Hubbard model with first-, second- and third-nearest-neighbor hopping terms (t, t’ and t”, respectively) by using the Gutzwiller-Jastrow-type wave function taking account of three-body correlations on a triangle, which is efficient for frustrated systems. The condensation energies of the vertical stripes and the homogeneous SC were computed as a function of t’/t with a fixed relation t”= –t’/2. We have found that, at the nearly optimal doping with moderately strong on-site Coulomb interaction, the state of maximum condensation energy switches from the vertical stripes to the homogeneous dSC as |t’/t| increases.
With the high-Tc cuprates in mind, properties of correlated d-wave superconducting (SC) states are studied for a Hubbard model on square lattices with a diagonal transfer (t-t’-U model), using a variational Monte Carlo method. We employ a simple wave function, which includes crucial parameters, in particular, a doublon-holon (D-H) binding factor important for correlated SC and normal states as doped Mott insulators. We first check that the range of dominant superconductivity is limited to a strongly correlated regime (U>W, U: onsite correlation strength, W: band width), and coincides with the effective range of the D-H binding factors. In this range of U/t and δ (doping rate), holons (in hole-doped cases) are classified into two types: doped holons and ones created as D-H pairs. Only the former holons participate in current, whereas the latter contribute to singlet-pair formation. Next, we show that the SC properties undergo a crossover at U=Uco∼W. For U<Uco, the behavior is appropriately interpreted with the conventional BCS mechanism, whereas for U>Uco (the regime of cuprates), a new idea is needed to understand the peculiar SC behavior.