Variational Monte Carlo study of ferromagnetism in the two-orbital Hubbard model on a square lattice

To understand effects of orbital degeneracy on magnetism, in particular effects of Hund's rule coupling, we study the two-orbital Hubbard model on a square lattice by a variational Monte Carlo method. As a variational wave function, we consider a Gutzwiller projected wave function for a staggered spin and/or orbital ordered state. We find a ferromagnetic phase with staggered orbital order around quarter-filling, i.e., electron number n=1 per site, and an antiferromagnetic phase without orbital order around half-filling n=2. In addition, we find that another ferromagnetic phase without orbital order realizes in a wide filling region for large Hund's rule coupling. These two ferromagnetic states are metallic except for quarter filling. We show that orbital degeneracy and strong correlation effects stabilize the ferromagnetic states.Comment: 4 pages, 2 figure

Weyl semimetallic state in the Rashba-Hubbard model

We investigate the Hubbard model with the Rashba spin-orbit coupling on a square lattice. The Rashba spin-orbit coupling generates two-dimensional Weyl points in the band dispersion. In a system with edges along [11] direction, zero-energy edge states appear, while no edge state exists for a system with edges along an axis direction. The zero-energy edge states with a certain momentum along the edges are predominantly in the up-spin state on the right edge, while they are predominantly in the down-spin state on the left edge. Thus, the zero-energy edge states are helical. By using a variational Monte Carlo method for finite Coulomb interaction cases, we find that the Weyl points can move toward the Fermi level by the correlation effects. We also investigate the magnetism of the model by the Hartree-Fock approximation and discuss weak magnetic order in the weak-coupling region.Comment: 9 pages, 11 figure

Multipole ordering in f-electron systems

In order to investigate multipole ordering in f-electron systems from a microscopic viewpoint, we study the so-called \Gamma_8 models on three kinds of lattices, simple cubic (sc), bcc, and fcc, based on a j-j coupling scheme with f-electron hopping integrals through (ff\sigma) bonding. From the \Gamma_8 model, we derive an effective model for each lattice structure by using the second-order perturbation theory with respect to (ff\sigma). By further applying mean-field theory to the effective model, we find a \Gamma_{3g} antiferro-quadrupole transition for the sc lattice, a \Gamma_{2u} antiferro-octupole transition for the bcc lattice, and a longitudinal triple-q \Gamma_{5u} octupole transition for the fcc lattice.Comment: 2 pages, 3 figure

Ferromagnetism and orbital order in the two-orbital Hubbard model

We investigate spin and orbital states of the two-orbital Hubbard model on a square lattice by using a variational Monte Carlo method at quarter-filling, i.e., the electron number per site is one. As a variational wave function, we consider a Gutzwiller projected wave function of a mean-field type wave function for a staggered spin and/or orbital ordered state. Then, we evaluate expectation value of energy for the variational wave functions by using the Monte Carlo method and determine the ground state. In the strong Coulomb interaction region, the ground state is the perfect ferromagnetic state with antiferro-orbital (AF-orbital) order. By decreasing the interaction, we find that the disordered state becomes the ground state. Although we have also considered the paramagnetic state with AF-orbital order, i.e., purely orbital ordered state, and partial ferromagnetic states with and without AF-orbital order, they do not become the ground state.Comment: 4 pages, 1 figure, accepted for publication in Journal of Physics: Conference Serie