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arXiv:2312.05860 · Physical review. B./Physical review. B

Quantitative determination of the orbital-selective Mott transition and quantum entanglement in the orbital-selective Mott phase

Yuekun Niu, Yu Hua Ni, Haishan Zhang, Liang Qiu, Jianli Wang, Leiming Chen, Yun Song, Shiping Feng

Published Jul 17, 2024• 0 citations
arXivHTMLPDF

Abstract

We examine the orbital-selective Mott transition in the non-hybridized two-band Hubbard model using the dynamical mean-field theory. We find that the orbital-selective Mott transition could be quantitatively depicted by the local two-qubit fidelity. Furthermore, within the orbital-selective Mott phase, the combined characteristics of the two orbitals lead to the presence of quantum entanglement, which is characterized by the non-semi-integer values of local two-qubit fidelity. It is demonstrated that the Hund's coupling results in the ground states of both wide and narrow bands exhibiting the specific superposition states, indicating the existence of quantum entanglement within orbital-selective Mott phase. Without Hund's coupling, there are no specific superposition states, nor does quantum entanglement occur within the orbital-selective Mott phase. The mechanisms underlying the orbital-selective Mott transition show prominent variations depending on the presence or absence of Hund's coupling and its transverse terms.

DOI
10.1103/physrevb.110.045131

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We examine the orbital-selective Mott transition in the non-hybridized two-band Hubbard model using the dynamical mean-field theory. We find that the orbital-selective Mott transition could be quantitatively depicted by the local two-qubit fidelity. Furthermore, within the orbital-selective Mott phase, the combined characteristics of the two orbitals lead to the presence of quantum entanglement, which is characterized by the non-semi-integer values of local two-qubit fidelity. It is demonstrated that the Hund's coupling results in the ground states of both wide and narrow bands exhibiting the specific superposition states, indicating the existence of quantum entanglement within orbital-selective Mott phase. Without Hund's coupling, there are no specific superposition states, nor does quantum entanglement occur within the orbital-selective Mott phase. The mechanisms underlying the orbital-selective Mott transition show prominent variations depending on the presence or absence of Hund's coupling and its transverse terms.
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.
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.
Recent advances in the field of quantum Monte Carlo simulations for impurity problems allow---within dynamical mean field theory---for a more thorough investigation of the two-band Hubbard model with a narrow-wide band and SU(2)-symmetric Hund's exchange. The nature of this transition has been controversial, and we establish that an orbital-selective Mott-Hubbard transition exists. The wide band still shows metallic behavior after the narrow band became insulating---not a pseudogap as for an Ising Hund's exchange. The coexistence of two solutions with a metallic wide band and an insulating or metallic narrow band indicates, in general, first-order transitions.
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.
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 effects of crystal field splitting in a doped two-band Hubbard model with different bandwidths within dynamical mean-field theory (DMFT), using a quantum Monte Carlo impurity solver. In addition to an orbital-selective Mott phase (OSMP) of the narrow band, which is adiabatically connected with the well-studied OSMP in the half-filled case without crystal field splitting, we find, for sufficiently strong interaction and a suitable crystal field, also an OSMP of the wide band. We establish the phase diagram (in the absence of magnetic or orbital order) at moderate doping as a function of interaction strength and crystal field splitting and show that also the wide-band OSMP is associated with non-Fermi-liquid behavior in the case of Ising-type Hund rule couplings. Our numerical results are supplemented by analytical strong-coupling studies of spin order and spectral functions at integer filling.