The Quantum Monte Carlo simulation of the two-dimensional Emery model of the CuO2 plane of hight Tc superconductors were performed. The method based on the direct-space proposed by Suzuki and Hirsch was used. Contrary to the method based on the Hubbard-Stratonovich transformation, the states generated by this method are basis states in occupation number representation, i. e. configurations of fermions can be observed on real two-dimensional array.Energy and specific heat were computed for different dopings. Specific heat curves show peaks at low temperature which could be assigned to electronic transitions. Quantity similar to current-current correlation function were computed. The static electric conductivity curves obtained by this way show metal-insulator transitions and two different metallic behaviours. On the direct-space states generated at low temperature and zero doping, the fermions form antiferromagnetic loops while they form antiferromagnetic chains for other dopings. The loops seem to appear when the conductivity becomes zero while yhe conductivity increases with the numbers of chains but superconductivity is not unambiguously evident.
The Quantum Monte Carlo simulation of the two-dimensional Emery model of the CuO2 plane of hight Tc superconductors were performed. The method based on the direct-space proposed by Suzuki and Hirsch was used. Contrary to the method based on the Hubbard-Stratonovich transformation, the states generated by this method are basis states in occupation number representation, i. e. configurations of fermions can be observed on real two-dimensional array.Energy and specific heat were computed for different dopings. Specific heat curves show peaks at low temperature which could be assigned to electronic transitions. Quantity similar to current-current correlation function were computed. The static electric conductivity curves obtained by this way show metal-insulator transitions and two different metallic behaviours. On the direct-space states generated at low temperature and zero doping, the fermions form antiferromagnetic loops while they form antiferromagnetic chains for other dopings. The loops seem to appear when the conductivity becomes zero while yhe conductivity increases with the numbers of chains but superconductivity is not unambiguously evident.
The Quantum Monte-Carlo simulations of the two-dimensional Hubbard model are presented for the half filling. The method based on the direct-space proposed by Suzuki and al., and Hirsch and al. was used. The states generated by this method are basis states in occupation number representation built with Wannier states localised on each site of the square array. The configurations of fermions can be observed on the real 2D array. An antiferromagnetic factor is defined and calculated for each temperature. The curves of energy, specific heat, conducivity and antiferromagnetic factor are presented for different values of the repulsive coulombian on site interaction U. There is a metal-insulator transition at low temperature for small values of U. This transition corresponds with a paramagnetic-ferromagnetic first order transition. Indeed, for these interaction values, the energy curves show a gap which is a characteristic of a first order transition. An hysteresis phenomenon appears on the conductivity curves. There is a behaviour change for U/t=3.5. For the values U>3.5 there is ferromagnetic-paramagnetic change without observable effect on the energy and the specific heat. The metal-insulator transition does not exist any more, the conductivity stays very small. Isotherms of the physical quantities versus U/t show a transition which seems to be the metal-insulator Mott transition. These results allow to draw a phase diagram with two first order transition lines.
The Quantum Monte Carlo simulations of the ionic Hubbard model on a two-dimensional square lattice at half filling were performed. The method based on the direct-space, proposed by Suzuki and al., Hirsch and al., was used. Cycles of increasing and decreasing values of the Coulomb interaction $ U $ were performed for fixed temperature ($ kT=0.01 $). Results indicate that, at low temperature, the two insulator phases are separated by a metallic phase for weak to intermediate values of the staggered potential $ Δ$. For large Coulomb repulsion the system is in a Mott insulator with an antiferromagnetism order. On increasing and decreasing the Coulomb interaction $ U $ the metal-Mott insulator transition shows an hysteresis phenomenon while the metal-band insulator transition is continue. For large $ Δ$ it seems that the metallic region shrinks to a single metallic point. However, the band insulator to the Mott insulator transition is not direct for the studied model. A phase diagram is drawn for the temperature $ kT=0.01 $. For $ Δ=0.5 $ cycles of increasing and decreasing temperature were programmed for different values of the Coulomb interaction $ U $ . A behaviour change appears for $ U\simeq 1.75 $. This suggests that a crossover line divides the metallic region of the phase diagram.
We study the three-band Hubbard model for the cuprate superconductors using Quantum Monte Carlo simulations and the fluctuation exchange approximation including a self-consistent many-body renormalization of the single-particle propagator. The energy dispersion of the low-lying one-particle excitations is in very good agreement with spectroscopic measurements for a hole doping concentration δ = 0.25 of the CuO2 planes. At the same doping, we examine the spin susceptibility yielding a non-ordered phase with short-range incommensurate fluctuations near the antiferromagnetic wave vector. In the superconducting regime, the interaction vertex for the pairing correlation function in the extended s-wave channel shows a maximum for δ = 0.20, resembling the dependence of transition temperature Tc on doping.
In this paper, the stochastic series expansion quantum Monte Carlo method is employed to investigate the thermodynamic properties of hardcore Bose-Hubbard model in two-dimensional space. The two-dimensional hardcore Bose-Hubbard model can be mapped into the two-dimensional antiferromagnetic quasi-Heisenberg model under transform of bosonic operators. There is an additional term which is proportional to the total number of sites compared with real Heisenberg model and it is difficult for simulation. Using a nonlocal operator-loop update, it allows one to simulate thousands of sites. Our simulation results show that, first, energy decreases with the increase of density of particles in a range from 0 to 0.5, and finally approaches to a fixed value. Moreover, with the size of square lattice increasing, energy also increases. Second, when we fix the system size, energy and magnetization increase with temperature, but not with of chemical potential. When we increase the system size, energy increases, while, the magnetization decreases. Third, specific heat is independent of chemical potential, but it dramatically increases with temperature and approaches to a peak, then decreases slowly. According to Landau theory of superfluidity, the tends of curve for energy and specific heat fit the research of He II in the Landau two-fluid model. Fourth, different square lattice linear system sizes have a little influence on tiny differences to the reciprocal of uniform susceptibility. There are small fluctuations in a range from 0 to 0.5(J/kB), where J is the coupling energy, kB is the Boltzmann constant, but the reciprocal of uniform susceptibility increases with temperature increasing in a range from 0.5 to 2(J/kB). The tends of curve are similar to those of Kondo effect.
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.
It is important to understand the phase diagram of electronic states in the CuO2 plane to clarify the mechanism of high-temperature superconductivity. We investigate the ground state of electronic models with strong correlation by employing the optimization variational Monte Carlo method. We consider the two-dimensional Hubbard model as well as the three-band [Formula: see text]–[Formula: see text] model. We use the improved wave function that takes account of inter-site electron correlation to go beyond the Gutzwiller wave function. The ground state energy is lowered considerably, which now gives the best estimate of the ground state energy for the two-dimensional Hubbard model. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We investigate the competition between the antiferromagnetic state and superconducting state by varying the Coulomb repulsion [Formula: see text], the band parameter [Formula: see text] and the electron density [Formula: see text] for the Hubbard model. We show phase diagrams that include superconducting and antiferromagnetic phases. We expect that high-temperature superconductivity occurs near the boundary between antiferromagnetic phase and superconducting one. Since the three-band [Formula: see text]–[Formula: see text] model contains many-band parameters, high-temperature superconductivity may be more likely to occur in the [Formula: see text]–[Formula: see text] model than in single-band models.