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arXiv:1412.2174 · Physical Review B

Quantum phase transition between orbital-selective Mott states in Hund's metals

Julián Rincón, Adriana Moreo, Gonzalo Álvarez, Elbio R. Dagotto

Published Dec 5, 2014• 24 citations
arXivHTMLPDF

Abstract

We report a quantum phase transition between orbital-selective Mott states, with different localized orbitals, in a Hund's metals model. Using the density matrix renormalization group, the phase diagram is constructed varying the electronic density and Hubbard $U$, at robust Hund's coupling. We demonstrate that this transition is preempted by charge fluctuations and the emergence of free spinless fermions, as opposed to the magnetically driven Mott transition. The Luttinger correlation exponent is shown to have a universal value in the strong-coupling phase, whereas it is interaction dependent at intermediate couplings. At weak coupling we find a second transition from a normal metal to the intermediate-coupling phase.

DOI
10.1103/physrevb.90.241105

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We report a quantum phase transition between orbital-selective Mott states, with different localized orbitals, in a Hund's metals model. Using the density matrix renormalization group, the phase diagram is constructed varying the electronic density and Hubbard UUU, at robust Hund's coupling. We demonstrate that this transition is preempted by charge fluctuations and the emergence of free spinless fermions, as opposed to the magnetically driven Mott transition. The Luttinger correlation exponent is shown to have a universal value in the strong-coupling phase, whereas it is interaction dependent at intermediate couplings. At weak coupling we find a second transition from a normal metal to the intermediate-coupling phase.
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.
We study the Mott metal-insulator transition in the two-band Hubbard model with different hopping amplitudes t1 and t2 for the two orbitals on the two-dimensional square lattice by using non-magnetic variational wave functions, similarly to what has been considered in the limit of infinite dimensions by dynamical mean-field theory. We work out the phase diagram at half filling (i.e. two electrons per site) as a function of R = t2/t1 and the on-site Coulomb repulsion U, for two values of the Hund's coupling J = 0 and J/U = 0.1. Our results are in good agreement with previous dynamical mean-field theory calculations, demonstrating that the non-magnetic phase diagram is only slightly modified from infinite to two spatial dimensions. Three phases are present: a metallic one, for small values of U, where both orbitals are itinerant; a Mott insulator, for large values of U, where both orbitals are localized because of the Coulomb repulsion; and the so-called orbital-selective Mott insulator (OSMI), for small values of R and intermediate Us, where one orbital is localized while the other one is still itinerant. The effect of the Hund's coupling is two-fold: on one side, it favors the full Mott phase over the OSMI; on the other side, it stabilizes the OSMI at larger values of R.
We study nonlocal correlations in a three-orbital Hubbard model defined on an extended one-dimensional chain using determinant quantum Monte Carlo and density matrix renormalization group methods. We focus on a parameter regime with robust Hund's coupling, which produces an orbital selective Mott phase (OSMP) at intermediate values of the Hubbard UUU, as well as an orbitally ordered ferromagnetic insulating state at stronger coupling. An examination of the orbital- and spin-correlation functions indicates that the orbital ordering occurs before the onset of magnetic correlations in this parameter regime as a function of temperature. In the OSMP, we find that the self-energy for the itinerant electrons is momentum dependent, indicating a degree of nonlocal correlations while the localized electrons have largely momentum independent self-energies. These nonlocal correlations also produce relative shifts of the holelike and electronlike bands within our model. The overall momentum dependence of these quantities is strongly suppressed in the orbitally ordered insulating phase.
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.
Quantum orbital-selective Mott (OSM) transitions are investigated within dynamical mean-field theory based on a two-orbital Hubbard model with different bandwidth at half filling. We find two distinct OSM phases both showing coexistence of itinerant electrons and localized spins, dependent on whether the Hund's coupling is full or of Ising type. The critical values and the nature of the OSM transitions are efficiently determined by entanglement entropy. We reveal that vanishing of the Kondo energy scale evidenced by absence of local spin fluctuations at low frequency in local dynamical spin susceptibility is responsible for the appearance of non-Fermi-liquid OSM phase in Ising Hund's coupling case. We argue that this scenario can also be applied to account for emergent quantum non-Fermi liquid in the one-band Hubbard model when short-range antiferromagnetic order is considered.
Using the density matrix renormalization group technique we study the effect of spin-orbit coupling on a three-orbital Hubbard model in the (t2g)4{({t}_{2g})}^{4}(t2g​)4 sector and in one dimension. Fixing the Hund coupling to a robust value compatible with some multiorbital materials, we present the phase diagram varying the Hubbard UUU and spin-orbit coupling $\ensuremath{\lambda}$, at zero temperature. Our results are shown to be qualitatively similar to those recently reported using the dynamical mean-field theory in higher dimensions, providing a robust basis to approximate many-body techniques. Among many results, we observe an interesting transition from an orbital-selective Mott phase to an excitonic insulator with increasing $\ensuremath{\lambda}$ at intermediate UUU. In the strong UUU coupling limit, we find a nonmagnetic insulator with an effective angular momentum $\ensuremath{\langle}{({\mathbf{J}}^{\mathrm{eff}})}^{2}\ensuremath{\rangle}\ensuremath{\ne}0$ near the excitonic phase, smoothly connected to the $\ensuremath{\langle}{({\mathbf{J}}^{\mathrm{eff}})}^{2}\ensuremath{\rangle}=0$ regime. We also provide a list of quasi-one-dimensional materials where the physics discussed in this paper could be realized.