The authors have used an exact diagonalization technique to explore the ground-state phase diagram of the two-dimensional Holstein-t-J model near half filling. The nature of the ground state is analysed, calculating self consistently the local lattice distortions, on-site spin and charge densities, as well as the magnetic structure form factor. They demonstrate that doped holes tend to form hole-polaron or bipolaron states. Compared to that in the uncorrelated model (spinless fermions), the critical electron-phonon coupling strength for the self-trapping transition of the doped charge carriers is considerably reduced by the antiferromagnetic exchange interaction. The relevance to the cuprate superconductors is discussed.
We investigate the Hubbard model on a two-dimensional cluster of 18 sites using Lanczos algorithm for different strengths of Coulomb repulsion in the low doping region. Energies and correlation functions are given for half-filling and two holes. In the strong coupling regime we compare our results with the $t\ensuremath{-}J$ model. We confirm the tendency of holes to repel, although a significant value of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductive order parameter is measured. These data represent a benchmark for future quantum simulations.
The ground state of two-dimensional t – J model including superconductivity and antiferromagnetism is studied using a new type of analytic estimation of the effect of strong correlation. The method is an extension of the Gutzwiller approximation which gives renormalization of parameters, t and J , due to the Gutzwiller projection operator excluding double occupancies. It is shown that the essential point of the renormalization is its dependence on the expectation values of superconductivity and antiferromagnetic moment. In special the renormalization factor is anisotropic in spin space, which leads to a reliable estimate of antiferromagnetic order parameters in the phase diagram, in contrast to the conventional slave-boson mean-field theory. The obtained phase diagram shows the coexistence of antiferromagnetism and d x 2 - y 2 -wave superconductivity for the doping rate, δ, less than 10%. At half-filling, the renormalization of the J -term represents some aspects of quantum spin nature. For the finite doping case, there are two kinds of superconducting order parameters. The variational order parameter of the d-wave superconductivity increases as the doping rate decreases, which will correspond to the experimentally observed superconducting gap. In contrast, the actual expectation value of superconducting order parameter is proportional to δ in underdoped region and has a maximum near δ=0.11, which probably determines T c . We also speculate that the ground-state antiferromagnetic order, being destroyed at finite temperatures, gives the energy and temperature scale of the pseudogap. Applications to the inhomogeneous systems such as the vortex state and stripe state are discussed.
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.
The quantum Monte Carlo method is used to reexamine superconductivity in the single-band Hubbard model in two dimensions. Instead of the conventional pairing, we consider a ``correlated pairing,'' 〈c-${\mathrm{tilde}}_{\mathrm{i}\mathrm{\ensuremath{\uparrow}}}$c-${\mathrm{tilde}}_{{\mathrm{i}}^{|\mathrm{I}\mathrm{H}}\mathrm{\ensuremath{\downarrow}}}$〉 with c-${\mathrm{tilde}}_{\mathrm{i}\mathrm{\ensuremath{\sigma}}}$\ensuremath{\equiv}${\mathrm{c}}_{\mathrm{i}\mathrm{\ensuremath{\sigma}}}$(1-${\mathrm{n}}_{\mathrm{i}\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\sigma}}}$), which is inferred from the t-J model, the strong-coupling limit of the Hubbard model. The pairing in the d-wave channel is found to possess both a divergence like 1/T in the pairing susceptibility and a growth of the ground-state pairing correlation with sample size, indicating an off-diagonal long-range order near (but not exactly at) half-filling.
We investigate the ground-state properties of two strongly-correlated systems: the two-dimensional
t−J model that can be used to study the high-temperature superconducting phase in the doped antiferromagnet, and the frustrated N\'eel antiferromagnet described by the
J1−J2 Heisenberg model on the square lattice, which is widely considered as the prototype model for spin frustration. In this thesis, we apply to these two systems state-of-the-art quantum Monte Carlo techniques, including the variational and the Green's function Monte Carlo with the fixed-node approximation. Few Lanczos steps are used to systematically improve the accuracy of the trial wave functions. By introducing a suitable regularization scheme for the variational calculations with few Lanczos steps, stable and controllable simulations can be performed up to very large cluster sizes with very good accuracy. In the two-dimensional
t−J model at
J/t=0.4, we show that the accuracy of the Gutzwiller-projected variational state (containing
dx2−y2 pairing) can be improved much by few Lanczos steps; in addition, the fixed-node Monte Carlo with these systematically improvable trial wave functions gives results that are comparable with the best accurate DMRG ones. Our main outcome is that the ground state is homogeneous and no evidence of stripes is detected around the doping
δ=1/8. Indeed, our best approximation to the ground state does not show any tendency towards charge inhomogeneity. Furthermore, our results show that a uniform state containing superconductivity and antiferromagnetism is stabilized at low hole doping, i.e.,
δ≲0.1. In the
J1−J2 Heisenberg model on the square lattice, we use the projected mean-field state that is built from Abrikosov fermions having a
Z2 gauge structure and four Dirac points in the spinon spectrum. No spin or dimer order is found in the strongly frustrated regime and our calculations imply that a spin liquid phase may faithfully represent the exact ground state around
J2/J1=0.5. The few Lanczos step technique is used to systematically improve the accuracy of the variational states both for the ground state and for few relevant low-energy excitations. This procedure allows us to estimate, in a valuable and systemic way, the spin gaps within thermodynamical limit and to show a solid evidence of an unconventional gapless excitation spectrum in the strongly frustrated regime, i.e.,
J2/J1≃0.5. In particular, we found gapless triplet excitations at momenta
(π,0) and
(0,π), which are compatible with the presence of four Dirac points at momenta
(±2π,±2π) in the spinon spectrum.