Correlated-Electron Systems and High-Temperature Superconductivity

Abstract

We present recent theoretical results on superconductivity in correlated-electron systems, especially in the twodimensional 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 Carlo method. 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 YBa 2 Cu 3 O 7 . 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  ,  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 4 4  period checkerboard spin modulation, that is characterized by multi Q vectors, is indeed stabilized. We have further performed an investigation by using a quantum Monte Carlo method, 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.

Superconductivity, Antiferromagnetism, and Kinetic Correlation in Strongly Correlated Electron Systems

“…It is difficult to observe a clear sign of superconductivity in weakly correlated region; for example, is less than 6 , by numerical calculations. This is consistent with the results obtained by quantum Monte Carlo methods [17,39,45].…”

“…where indicates the kinetic term of the Hamiltonian = ∑ † and is a real constant which is the variational parameter to be optimized [37][38][39]. This wave function is a first approximation to the wave function used in quantum Monte Carlo method [40].…”

Mechanism of High-Temperature Superconductivity in Correlated-Electron Systems

“…72) A variational Monte Carlo method is used to examine the ground state properties of strongly correlated electron systems, where we calculate the expectation values exactly using a numerical method. [28][29][30][31][36][37][38][39][40][41] We introduced the wave function of exp(−S )-type in the study of superconductivity in the Hubbard model. [73][74][75] This wave function is very excellent in the sense that the energy expectation value is lower than that of any other wave functions.…”

Crossover Induced Electron Pairing and Superconductivity by Kinetic Renormalization in Correlated Electron Systems

“…It appears very hard to elucidate the phase diagram of the d-p model because of strong correlation between electrons. We often examine simplified models such as the two-dimensional single-band Hubbard model [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] or ladder model [39][40][41][42][43] as an attempt to make clear the phase diagram of correlated electron systems.…”

“…A variational Monte Carlo method is a useful method to investigate electronic properties of strongly correlated electron systems by calculating the expectation values numerically [26][27][28][29][30][31]. A variational wave function can be improved by introducing new variational parameters to control the electron correlation.…”