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arXiv:1509.01415 · Physical Review B

Slope-reversed Mott transition in multiorbital systems

Aaram J. Kim, M. Y. Choi, Gun Sang Jeon

Published Sep 14, 2015• 1 citation
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Abstract

We examine finite-temperature phase transitions in the two-orbital Hubbard model with different bandwidths by means of the dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. It is found that there emerges a peculiar slope-reversed first-order Mott transition between the orbital-selective Mott phase and the Mott insulator phase in the presence of Ising-type Hund's coupling. The origin of the slope-reversed phase transition is clarified by the analysis of the temperature dependence of the energy density. It turns out that the increase of Hund's coupling lowers the critical temperature of the slope-reversed Mott transition. Beyond a certain critical value of Hund's coupling the first-order transition turns into a finite-temperature crossover. We also reveal that the orbital-selective Mott phase exhibits frozen local moments in the wide orbital, which is demonstrated by the spin-spin correlation functions.

DOI
10.1103/physrevb.92.125127

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We examine finite-temperature phase transitions in the two-orbital Hubbard model with different bandwidths by means of the dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. It is found that there emerges a peculiar slope-reversed first-order Mott transition between the orbital-selective Mott phase and the Mott insulator phase in the presence of Ising-type Hund's coupling. The origin of the slope-reversed phase transition is clarified by the analysis of the temperature dependence of the energy density. It turns out that the increase of Hund's coupling lowers the critical temperature of the slope-reversed Mott transition. Beyond a certain critical value of Hund's coupling the first-order transition turns into a finite-temperature crossover. We also reveal that the orbital-selective Mott phase exhibits frozen local moments in the wide orbital, which is demonstrated by the spin-spin correlation functions.
We examine whether the Mott transition of a half-filled, two-orbital Hubbard model with unequal bandwidths occurs simultaneously for both bands or whether it is a two-stage process in which the orbital with narrower bandwith localizes first (giving rise to an intermediate ``orbital-selective'' Mott phase). This question is addressed using both dynamical mean-field theory and a representation of fermion operators in terms of slave quantum spins, followed by a mean-field approximation (similar in spirit to a Gutzwiller approximation). In the latter approach, the Mott transition is found to be orbital selective for all values of the Coulomb exchange (Hund) coupling JJJ when the bandwidth ratio is small and only beyond a critical value of JJJ when the bandwidth ratio is larger. Dynamical mean-field theory partially confirms these findings, but the intermediate phase at J=0J=0J=0 is found to differ from a conventional Mott insulator, with spectral weight extending down to arbitrary low energy. Finally, the orbital-selective Mott phase is found, at zero temperature, to be unstable with respect to an interorbital hybridization VVV and replaced at small VVV by a state with a large effective mass (and a low quasiparticle coherence scale) for the narrower band.
We study the Mott transition in the three-orbital Hubbard model. To investigate how the orbital level splitting and the Ising-type Hund's coupling affect the Mott transition in the case of two electrons per site, we use the dynamical mean-field theory combined with continuous-time quantum Monte Carlo simulations. The calculation of the double occupancy reveals that the critical interaction strength separating a metallic phase and two kinds of insulating phases shows a nonmonotonic behavior as a function of the level splitting. We find that this behavior is characteristic for 1/31/31/3 filling, in comparison with the preceding results for different fillings and for two-orbital models. Strong competition between the two insulators results in an intriguing first-order transition to an insulating phase having intermediate characters between Mott and band insulators. It is also found that the two insulators show different behaviors in the phase boundary with the metallic phase in the interaction-temperature plane, which is reflected in a difference in the quasiparticle behavior around the transition. We also discuss the orbital selective Mott transition for larger Hund's coupling, which is compared with previous study at zero temperature.
Mott transitions in the two-orbital Hubbard model with different bandwidths are investigated at finite temperatures. By means of the self-energy functional approach, we discuss the stability of the intermediate phase with one orbital localized and the other itinerant, which is caused by the orbital-selective Mott transition (OSMT). It is shown that the OSMT realizes two different coexistence regions at finite temperatures in accordance with the recent results of Liebsch. We further find that the particularly interesting behavior emerges around the special condition U=U′U=U'U=U′ and J=0, which includes a new type of the coexistence region with three distinct states. By systematically changing the Hund coupling, we establish the global phase diagram to elucidate the key role played by the Hund coupling on the Mott transitions.
The anisotropic degenerate two-orbital Hubbard model is studied within dynamical mean-field theory at low temperatures. High-precision calculations on the basis of a refined quantum Monte Carlo (QMC) method reveal that two distinct orbital-selective Mott transitions occur for a bandwidth ratio of 2, even in the absence of spin-flip contributions to the Hund exchange. The second transition---not seen in earlier studies using QMC, iterative perturbation theory, and exact diagonalization---is clearly exposed in a low-frequency analysis of the self-energy and in local spectra.
We investigate the phase diagram of the spin-orbit-coupled three orbital Hubbard model at arbitrary filling by means of dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. We find that the spin-freezing crossover occurring in the metallic phase of the nonrelativistic multiorbital Hubbard model can be generalized to a J-freezing crossover, with J=L+S, in the spin-orbit-coupled case. In the J-frozen regime the correlated electrons exhibit a nontrivial flavor selectivity and energy dependence. Furthermore, in the regions near n=2 and n=4 the metallic states are qualitatively different from each other, which reflects the atomic Hund's third rule. Finally, we explore the appearance of magnetic order from exciton condensation at n=4 and discuss the relevance of our results for real materials.
Using the dynamical mean field theory with Lanczos method as its impurity solver, we study the orbital-selective Mott transition (OSMT) in the two-orbital J model and Jz model. In the multi-orbital systems, the Mott metal-insulator transition occurs successively when the widths of the bands are different. As the narrow orbital becomes Mott insulator while the wide orbital is still in metallic phase, we find an orbital-selective Mott phase (OSMP). There are two different Hubbard models that are frequently used to describe the OSMT, which are named J model and Jz model, respectively. The J Model is composed of the whole Hund's rule coupling terms, including the spin-flip term, the pair-hopping term and the Ising type Hund's rule coupling term. However, there is only Ising type Hund's rule coupling term in the Jz model.#br#We study the ratio of bandwidth W2/W1 on the OSMT by analyzing the results of the density of states and quasi-particle weight. Comparing the phase diagrams obtained from the J and Jz models with the Hund's rule coupling J(Jz)=U/4, we find that the OSMP region of the J model is much larger than that of the Jz model when W2/W1=0.5 or W2/W1=0.2. When the ratio of bandwidth increases to W2/W1=0.8, the OSMP disappears completely in the Jz model. However in the J model, we can still find the OSMT but the area of the OSMP shrinks significantly. Therefore, the OSMT happens more easily in the J model than in the Jz model.#br#In order to discuss the cooperative effect of the bandwidth and Hund's rule coupling on the OSMT, we compare the phase diagrams for different Hund's rule couplings J(Jz)=U/4 and J(Jz)=U/2. We find that when the bandwidth W2/W1≥q 0.7, the OSMT disappears in Jz model in the case of either Jz=U/4 or Jz=U/2. However, the OSMP always exists in the J model if the bandwidths of the two orbitals are different, suggesting that the rotation invariances of the Hund's rule couplings can protect the OSMP. Therefore, one should be more careful when using the Jz model instead of the J model to study the OSMP.