Magnetic and superconducting pairing correlation functions in a general class of Hubbard models, the t - J model and a single-band Hubbard model with additional bond - charge interaction are investigated. Some rigorous upper bounds of the corresponding correlation functions are obtained. It is found that the decay of the spin - spin correlation function with temperature in the general Hubbard models cannot be slower than the inverse square law at low temperatures and the inverse law at high temperatures, while the on-site pairing correlation function cannot be slower than the inverse law. An upper bound for the average energy of the t - J model is found. The upper bounds for the spin - spin and the electron pairing correlation functions in the t - J model as well as in the Hubbard model with bond - charge interaction are also obtained. These bounds are expected to provide certain standards for approximate methods. In some special cases, these bounds rule out the possibility of corresponding magnetic and pairing long-range order.
Magnetic and superconducting pairing correlation functions in a general class of Hubbard models, the t - J model and a single-band Hubbard model with additional bond - charge interaction are investigated. Some rigorous upper bounds of the corresponding correlation functions are obtained. It is found that the decay of the spin - spin correlation function with temperature in the general Hubbard models cannot be slower than the inverse square law at low temperatures and the inverse law at high temperatures, while the on-site pairing correlation function cannot be slower than the inverse law. An upper bound for the average energy of the t - J model is found. The upper bounds for the spin - spin and the electron pairing correlation functions in the t - J model as well as in the Hubbard model with bond - charge interaction are also obtained. These bounds are expected to provide certain standards for approximate methods. In some special cases, these bounds rule out the possibility of corresponding magnetic and pairing long-range order.
In a general class of one- and two-dimensional Hubbard models, we prove upper bounds for the two-point correlation functions at finite temperatures for electrons, electron pairs, and spin. The upper bounds decay exponentially in one dimension, and with power laws in two dimensions. The bounds rule out the possibility of the corresponding condensation of superconducting electron pairs, and of the corresponding magnetic ordering. Our method is general enough to cover other models such as the t-J model.
We have studied the superconducting, magnetic, and charge correlation functions and the spin excitation spectrum in the doped two-chain Hubbard model by projector Monte Carlo and Lanczos diagonalization methods. The exponent of the interchain singlet superconducting correlation function, \ensuremath{\gamma}, is found to be close to 2.0 as long as two distinct noninteracting bands cross the Fermi level. Magnetic and charge correlation functions decay more rapidly than or as fast as the interchain singlet superconducting correlation function along the chains. The superconducting correlation in the doped two-chain Hubbard model is the most long-range correlation studied here. Implications of the results for the possible universality class of the doped two-chain Hubbard model are discussed.
We study the effects of a bond-charge interaction (or correlated hopping) on the properties of the extended [i.e., with both on-site (U) and nearest-neighbor (V) repulsions] Hubbard model in one dimension at half-filling. Energy gaps and correlation functions are calculated by Lanczos diagonalization on finite systems. We find that, irrespective of the sign of the bond-charge interaction, X, the charge-density-wave (CDW) state is more robust than the spin-density-wave (SDW) state. A small bond-charge interaction term is enough to make the differences between the CDW and SDW correlation functions much less dramatic than when X=0. For X=t and fixed V2t (t is the uncorrelated hopping integral), there is an intermediate phase between a charge ordered phase and a phase corresponding to singly occupied sites, the nature of which we clarify: it is characterized by a succession of critical points, each of which corresponds to a different density of doubly occupied sites. We also find an unusual slowly decaying staggered spin-density correlation function, which is suggestive of some degree of ordering. No enhancement of pairing correlations was found for any X in the range examined. \textcopyright{} 1996 The American Physical Society.
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 Hubbard model has been widely used to describe magnetism due to itinerant electrons. However, except for the one-dimensional case, no exact solution of the model exists. We have studied the two-dimensional Hubbard model on a square lattice using a Monte Carlo simulation technique. Simulations were performed on lattices of up to 8×8 in spatial size. We will discuss results for thermodynamic properties and correlation functions as a function of temperature and interaction strength. For the half-filled band case, our results indicate that the system exhibits long-range antiferromagnetic order in the ground state for any nonzero interaction, although substantially reduced from the classical Néel state due to both charge and spin fluctuations. For the non-half-filled band case, our results suggest that no long-range magnetic order exists. We also don’t find any indication of short-ranged ferromagnetic correlations in the parameter range studied. We have also studied the predictions of various approximate treatments for this model, particularly the static approximation and the coherent potential approximation (CPA). By comparison with the Monte Carlo results, we discuss the validity of these schemes. Finally, we discuss the effect of changing the band structure on the magnetic properties of the system.
Using the constrained path Monte Carlo method, we simulated the two-dimensional, three-band Hubbard model to study pairing, charge, and spin correlations as a function of electron and hole doping and the Coulomb repulsion Vpd between charges on neighboring Cu and O lattice sites. As a function of distance, both the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave and extended s-wave pairing correlations decayed quickly. In the charge-transfer regime, increasing Vpd decreased the long-range part of the correlation functions in both channels, while in the mixed-valent regime, it increased the long-range part of the s-wave behavior but decreased that of the d-wave behavior. Still the d-wave behavior dominated. At a given doping, increasing Vpd increased the spin-spin correlations in the charge-transfer regime but decreased them in the mixed-valent regime. Also, increasing Vpd suppressed the charge-charge correlations between neighboring Cu and O sites. Electron and hole doping away from half-filling was accompanied by a rapid suppression of antiferromagnetic correlations. Our results suggest that adding a repulsive Vpd to the model does not enhance its tendency toward superconductivity even though the behavior of the spin structure factor is consistent with the properties of some high-temperature superconducting materials.