Orbital-selective Mott transitions in the anisotropic two-band Hubbard model at finite temperatures

Abstract

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. PACS numbers: 71.30.+h, 71.10.Fd, 71.27.+a The Mott-Hubbard metal-insulator transition -a nonperturbative correlation phenomenon -has been a subject of fundamental interest in solid state theory for decades. 1 Recently, this field became even more exciting by the discovery 2,3 of a two-step metal-insulator transition in the effective 3-band system Ca 2−x Sr x RuO 4 , for which the name orbital-selective Mott-transition (OSMT) was coined. 4 The Ca 2−x Sr x RuO 4 system was investigated theoretically in detail by Anisimov et al. 4 within the local density approximation (LDA and LDA+U) and within dynamical mean-field theory 5 (DMFT) solved using the non-crossing approximation (NCA). The underlying assumption of a correlation (rather than lattice-distortion) induced OSMT found support in further band structure calculations 6,7 and strong-coupling expansions for the localized electrons in the orbital-selective Mott phase. 8 Microscopic studies of the OSMT usually consider the 2-band Hubbard model H = H 1 + H 2 , wherehopping between nearest-neighbor sites i, j with amplitude t m for orbital m ∈ {1, 2}, intra-and interorbital Coulomb repulsion parametrized by U and U ′ , respectively, and Ising-type Hund's exchange coupling; n imσ = c † imσ c imσ for spin σ ∈ {↑, ↓}. In addition,contains spin-flip and pair-hopping terms (with1 ≡ 2, ↑ ≡↓ etc.). In cubic lattices, the Hamiltonian is invariant under spin rotation, J z = J ⊥ ≡ J; furthermore U ′ = U − 2J. In the following, we refer to H 1 + H 2 in this spin-isotropic case as the J-model and to the simplified Hamiltonian H 1 as the J z -model. Liebsch 9,10,11 questioned the OSMT scenario for Ca 2−x Sr x RuO 4 on the basis of finite-temperature quantum Monte Carlo (QMC) calculations (within DMFT) for the J z -model using J z = U/4, U ′ = U/2, and semielliptic "Bethe" densities of states with a bandwidth ratio W 2 /W 1 = 2. Additional studies using iterative perturbation theory (IPT) 11 seemed 12 to confirm his conclusion of a single Mott transition of both bands at the same critical U -value. Meanwhile, Koga et al. found an OSMT using exact diagonalization (ED), applied to the full J-model, 13 but not for the J z -model. 14 Consequently, the OSMT scenario was attributed to spin-flip and pairhopping processes.Very recently, four preprints appeared, 15,16,17,18 in which the OSMT was investigated in detail within the DMFT framework. Ref. 15 applied the Gutzwiller variational approach and ED to the J-model at...

Fast multi-orbital equation of motion impurity solver for dynamical mean field theory

“…Considering this broadening effect, our results are close to those obtained with the NRG method, but may have a slightly larger critical value of U . Next we present a comparison of results computed with the MO-EOM method to results achieved with the QMC method [31]. This comparison is visualized in Figure 10, The NRG data are taken from [35].…”

“…Here we first present calculated results for the case where the inter-orbital hybridization is neglected. In this case, our model Hamiltonian in (1) will return to the frequently studied Hamiltonian as shown in [31]. When the inter-orbital and intra-orbital Coulomb interaction strengths are identical, i.e., U 11 = U 22 = U 12σσ = U 12σσ and the Hund's rule coupling constant J = 0, we obtained the densities of states (DOS) for the halffilled system, as shown in Figure 2, where µ is the chemical potential and we have furthermore assumed that the two occupied orbital levels have the relation E 1 = E 2 .…”

“…If we neglect the hybridization between different orbitals (i.e., neglect the inter-site inter-orbital hopping in (1), and then the model Hamiltonian of (1) will return to the Hamiltonian in [31]), the above formula can be simplified by setting V * lmkσ = 0. In this sense, the approximation is similar to the single orbital case with arbitrary spin-orbital degeneracy N , where the degenerated electrons only hybridize with electrons having identical spin and orbital indices in the bath.…”

“…The first summation, which sums over two orbital indices and which differs from the usually studied form of the multi-orbital Hubbard model [31], is the hopping of electrons between different sites. The second (third) summation term is the on-site intra-orbital (inter-orbital) Coulomb interaction term, where the intra-orbital Coulomb interaction strength U ll and the inter-orbital Coulomb strength U lmσσ are free parameters that can be set all identical or all different in order to simulate different kinds of physical systems.…”

Quantum Phase Transition in the Two-Band Hubbard Model

“…For J 0 J, this would be a value typical for transition metal oxides which has been used in many previous calculations [11][12][13][14][15][16][17][18]20]. At small U, the density of states at the Fermi level, E F 0, satisfies the pinning condition, A 0 2= , approximately.…”