Mott Physics in Multicomponent Systems

Abstract

We investigate Hubbard-type models by means of the dynamical mean-field theory (DMFT) combined with the continuous-time quantum Monte Carlo (CTQMC) method. In this thesis, a great deal of effort has been devoted to investigating diverse facets of Mott physics. Interesting phenomena in strongly correlated electron systems emerge mostly when various energy scales compete with each other. We introduce additional degrees of freedom to the standard Hubbard model. The additional degrees of freedom include a staggered lattice potential, two orbitals, bilayer structure, and superconductivity. Depending on the model system, we extend the single-site DMFT to the multi-orbital one or employ cluster extension of the DMFT. In addition, two complementary versions of CTQMC, weak and strong coupling algorithm, are adopted as an impurity solver. We first consider a Mott transition of the Hubbard model in infinite dimensions. The DMFT is employed in combination with the CTQMC method for an accurate description at low temperatures. Through the use of the double occupancy and the energy density, which are directly measured via the CTQMC method, we construct the phase diagram. We pay particular attention to the construction of the first-order phase transition line (PTL) in the coexistence region of metallic and insulating phases. The resulting PTL is found to exhibit reasonable agreement with earlier finite-temperature results. We also show, by including systematically low-temperature data, that the PTL, which is obtained independently of the previous zero-temperature results, approaches monotonically the transition point reported in earlier zero-temperature studies. We next investigate paramagnetic metal-insulator transitions in the infinite-dimensional ionic Hubbard model at finite temperatures. By means of the DMFT with an impurity solver of the CTQMC, we show that an increase in the interaction strength brings about a crossover from a band insulating phase to a metallic one, followed by a first-order transition to the Mott insulating phase. The first-order transition turns into a crossover above a certain critical temperature, which becomes higher as the strength of the staggered lattice potential is increased. Further, analysis of the temperature dependence of the energy density discloses that the intermediate metallic phase is a Fermi liquid. It is also found that the metallic phase is stable against strong staggered potentials even at very low temperatures. Finite-temperature phase transitions are also examined in the two-orbital Hubbard model with Ising-type Hunds coupling. We adopt the multi-orbital extension of the DMFT combined with the strong coupling CTQMC. It is found that there emerges a peculiar reverse-sloped first-order Mott transition between the orbital-selective Mott phase and the Mott insulator phase. It turns out that the increase of Hunds coupling lowers the critical temperature of the reverse-sloped Mott transition. Beyond a certain critical value of Hunds coupling the first-order transition becomes a finite-temperature crossover. Bilayer effects in the Hubbard model are also studied in the dynamical cluster approximation (DCA) combined with the weak coupling algorithm of CTQMC. In the magnetic phase diagrams obtained in earlier studies, there still remain several controversial issues, particularly for weak on-site Coulomb interactions. In this study, we adopt eight-site clusters which preserve the underlying lattice symmetry. Magnetic properties and associated metal-insulator transitions are examined at low temperatures, and their implications to the ground-state phase diagram are also discussed. Finally, we discuss the BCS+U model which is a natural generalization of Gutzwiller-projected BCS model. For this study, we use the DCA combined with the weak coupling CTQMC and verify the reliability of our calculation by changing the cluster size. Our main focus is on the correlation effects of the phenomenological d-wave superconductor. The transition between the superconductor and the Mott insulator is observed as we change the interaction strength or doping concentration. We discuss the change in the spectral properties of the system during the transition.