To discuss correlation effects on the spin-orbit coupling (SOC), we investigate a two-orbital Hubbard model with SOC on a square lattice by using the variational Monte Carlo method.In the variational wave function, we consider an effective SOC constant λ eff in the one-body part of the variational wave function.In addition to the Gutzwiller parameters and doublon-holon binding factors, which describe correlation effects beyond the Hartree-Fock approximation, λ eff is treated as a variational parameter.We find that λ eff increases from the bare value by the Coulomb interaction.While the enhancement of λ eff is strongly suppressed in comparison with the result of the Hartree-Fock approximation, we find that λ eff can still become several times larger than the bare value.
We investigate the correlation effects on spin-orbit coupling (SOC) in a two-orbital Hubbard model on a square lattice by applying the variational Monte Carlo method. We consider an effective SOC constant
λeff in the one-body part of the variational wave function and mainly discuss the cases of the electron number per site
n=1, that is, quarter filling. We find that
λeff is proportional to the bare value
λ and depends on the electron-electron interactions through
(U′−J′) in a relatively wide parameter range in the paramagnetic (PM) phase, where
U′ is the interorbital Coulomb interaction and
J′ is the pair hopping interaction. Increasing the electron-electron interactions in the PM phase leads to a transition to an effective one-band state, in which the upper band becomes empty due to the enhanced
λeff. We also construct phase diagrams considering magnetic order. The carrier doping effect on
λeff is also investigated. We find that
λeff enhances in a strongly correlated region around the Mott transition point and it is necessary to include the correlation effects beyond the Hartree-Fock approximation to describe the enhanced SOC properly.
We investigate the Mott transition in a two-dimensional two-orbital Hubbard model on a square lattice at half filling by using the variational Monte Carlo method. As a variational trial wave function, we consider Gutzwiller's on-site correlations and nearest-neighbor doublon-holon correlations. We calculate the ground-state energy and the other physical quantities, all of which clearly signal a first-order Mott transition. We thus obtain the phase diagram at zero temperature, where we find the coexistence region of the metal and the Mott insulator. We discuss how Hund's coupling affects the nature of the Mott transition in this system.
We investigate the ground state properties of the one- and the two-dimensional Hubbard models using a new variational Monte Carlo method. By generalizing the Gutzwiller variational wave function (GF) to take into account an off-diagonal intersite correlation, we examine the metal-insulator transition mechanism at the half filling. As Kaplan et al. first pointed out, the binding mechanism between doubly occupied sites and empty sites plays a crucial role for this transition; we confirm this by examining the real space correlation function between these two kinds of sites. Results for the spin and the charge structure factors are presented as well as the momentum distribution function and are discussed in connection with the pairing effect. We also find that in less-than half filling, the improvements of the structure factors at 2 k F are realized as compared with GF results.
The mechanism of Mott transition in the Hubbard model on the square lattice is studied without explicit introduction of magnetic and superconducting correlations, using a variational Monte Carlo method. In the trial wave functions, we consider various types of binding factors between a doubly-occupied site (doublon, D) and an empty site (holon, H), like a long-range type as well as a conventional nearest-neighbor type, and add independent long-range D-D (H-H) factors. It is found that a wide choice of D-H binding factor leads to Mott transitions at critical values near the band width. We renew the D-H binding picture of Mott transitions by introducing two characteristic length scales, the D-H binding length l_{DH} and the minimum D-D distance l_{DD}, which we appropriately estimate. A Mott transition takes place at l_{DH}=l_{DD}. In the metallic regime (l_{DH}>l_{DD}), the domains of D-H pairs overlap with one another, thereby doublons and holons can move independently by exchanging the partners one after another. In contrast, the D-D factors give only a minor contribution to the Mott transition.
New variational wave functions are introduced to describe the Hubbard model in strong correlation. Intersite correlation (or Jastrow) factors are taken into account beyond the Gutzwiller wave function (GF). A study is made on the one-dimensional lattice and the two-dimensional square lattice at half-filling as well as less-than-half-filling. Much improvement can be achieved thereby in the description of physical quantities such as the momentum distribution and spin and charge density correlation functions. In addition, the ground state energy is lowered appreciably compared with the GF. In this connection, the Mott-Hubbard-type metal-insulator transition is also re-examined.