Crossover from Weakly to Strongly Correlated Regions in the Two-dimensional Hubbard Model — Off-diagonal Wave Function Monte Carlo Studies of Hubbard Model II —

Abstract

The ground state of the two-dimensional (2D) Hubbard model is investigated by adopting improved wave functions that take into account intersite electron correlation beyond the Gutzwiller ansatz. The ground-state energy is lowered considerably, giving the best estimate of the groundstate energy for the 2D Hubbard model. There is a crossover from weakly to strongly correlated regions as the on-site Coulomb interaction U increases. The antiferromagnetic correlation induced by U is reduced for hole doping when U is large, being greater than the bandwidth, thus increasing the kinetic energy gain. The spin and charge fluctuations are induced in the strongly correlated region. These antiferromagnetic and kinetic charge fluctuations induce electron pairings, which result in high-temperature superconductivity.

Mechanism of High-Temperature Superconductivity in Correlated-Electron Systems

“…In this paper, we use the wave function of exponential type in Equation (23) because the energy is further lowered when we use this wave function. 50) The wave function for the dp model is formulated similarly. An initial state ψ 0 contains many variational parameters (t d p ,t pp ,t ′ d , andǫ p −ǫ d ):…”

“…We uset d p = t d p as the energy unit. We consider the following wave function that is improved from the Gutzwiller wave function: 50,73,[186][187][188][189][190]…”

“…It is now certain that there is a superconducting phase in the strongly correlated region. 50) The simplest wave function of superconducting state with strong electron correlation is the Gutzwiller-projected BCS wave function:…”

“…[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. 50) The paper is organized as follows. In Section 2.1, we discuss the phonon mechanism of superconductivity.…”

Isotope shift of the ferromagnetic transition temperature in itinerant ferromagnets

“…SCES include, for example, cuprate high-temperature superconductors [1,2,3,4], heavy fermions [5,6,7,8], and organic conductors [9]. In the study of magnetism, the Hubbard model is regarded as one of the most fundamental models [10,11,12,13,14,15,16,17]. The electron-phonon interaction is also important in metals and even in correlated electron systems.…”