Dynamical Mean-Field Theory Plus Numerical Renormalization-Group Study of Spin-Orbital Separation in a Three-Band Hund Metal (original) (raw)
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Dynamical Mean Field Theory with the Density Matrix Renormalization Group
Physical Review Letters, 2004
A new numerical method for the solution of the Dynamical Mean Field Theory's self-consistent equations is introduced. The method uses the Density Matrix Renormalization Group technique to solve the associated impurity problem. The new algorithm makes no a priori approximations and is only limited by the number of sites that can be considered. We obtain accurate estimates of the critical values of the metal-insulator transitions and provide evidence of substructure in the Hubbard bands of the correlated metal. With this algorithm, more complex models having a larger number of degrees of freedom can be considered and finite-size effects can be minimized. PACS numbers: 71.10.Fd, 71.27.+a, 71.30.+h Great theoretical progress in our understanding of the physics of strongly correlated electron systems has been possible since the introduction of the Dynamical Mean Field Theory (DMFT) just over ten years now . This approach is based on the natural extension of the familiar classical mean-field theory of statistical mechanics to the treatment of models of strongly interacting electrons on a lattice. The DMFT solution of the model is exact in the limit of large lattice dimensionality or large connectivity [2, 3]. Since its introduction, DMFT has been widely adopted and was used for the investigation of a large variety of model Hamiltonians relevant for problems as diverse as colossal magneto-resistance, heavy fermions, metal-insulator transitions, etc. . A great deal of interest is currently centered around the ongoing efforts to incorporate DMFT as the local correlation physics "engine" for first-principle calculations of realistic compounds . At the heart of the DMFT method is the solution of an associated quantum impurity model where the environment of the impurity has to be determined self-consistently. Therefore the ability to obtain reliable DMFT solutions of lattice model Hamiltonians relies directly on the ability to solve quantum impurity models. Since solutions of general impurity models are usually not analytically tractable, one has to resort to numerical algorithms or approximate methods. Among the a priori exact numerical algorithms available we count the Hirsch-Fye Quantum Monte Carlo [6] method and Wilson's Numerical Renormalization Group (NRG) . The former is a finite-temperature method that is formulated in imaginary time and has been applied to a large variety of impurity models including the multi-orbital case that corresponds to correlated multi-band lattice Hamiltoni- * Present address: DFMC, Unicamp, Campinas, São Paulo, Brasil.
2016
The functional renormalization group (RG) in combination with Fermi surface patching is a well-established method for studying Fermi liquid instabilities of correlated electron systems. In this article, we further develop this method and combine it with mean-field theory to approach multiband systems with spin-orbit coupling, and we apply this to a tight-binding Rashba model with an attractive, local interaction. The spin dependence of the interaction vertex is fully implemented in a RG flow without SU(2) symmetry, and its momentum dependence is approximated in a refined projection scheme. In particular, we discuss the necessity of including in the RG flow contributions from both bands of the model, even if they are not intersected by the Fermi level. As the leading instability of the Rashba model, we find a superconducting phase with a singlet-type interaction between electrons with opposite momenta. While the gap function has a singlet spin structure, the order parameter indicates an unconventional superconducting phase, with the ratio between singlet and triplet amplitudes being plus or minus one on the Fermi lines of the upper or lower band, respectively. We expect our combined functional RG and mean-field approach to be useful for an unbiased theoretical description of the low-temperature properties of spin-based materials.
Frontiers in Physics, 2018
We implement an efficient numerical method to calculate response functions of complex impurities based on the Density Matrix Renormalization Group (DMRG) and use it as the impuritysolver of the Dynamical Mean Field Theory (DMFT). This method uses the correction vector to obtain precise Green's functions on the real frequency axis at zero temperature. By using a self-consistent bath configuration with very low entanglement, we take full advantage of the DMRG to calculate dynamical response functions paving the way to treat large effective impurities such as those corresponding to multi-orbital interacting models and multi-site or multi-momenta clusters. This method leads to reliable calculations of non-local self energies at arbitrary dopings and interactions and at any energy scale.
Hund's metal regimes and orbital selective Mott transitions in three band systems
Journal of Physics: Condensed Matter, 2019
We analyze the electronic properties of interacting crystal field split three band systems. Using a rotationally invariant slave boson approach we analyze the behavior of the electronic mass renormalization as a function of the intralevel repulsion U , the Hund's coupling J, the crystal field splitting, and the number of electrons per site n. We first focus on the case in which two of the bands are identical and the levels of the third one are shifted by ∆ > 0 with respect to the former. We find an increasing quasiparticle mass differentiation between the bands, for system away from half-filling (n = 3), as the Hubbard interaction U is increased. This leads to orbital selective Mott transitions where either the higher energy band (for 4 > n > 3) or the lower energy degenerate bands (2 < n < 3) become insulating for U larger than a critical interaction U c (n). Away from the half-filled case |n − 3| 0.3 there is a wide range of parameters for U < U c (n) where the system presents a Hund's metal phase with the physics dominated by the local high spin multiplets. Finally, we study the fate of the n = 2 Hund's metal as the energy splitting between orbitals is increased for different possible crystal distortions. We find a strong sensitivity of the Hund's metal regime to crystal fields due to the opposing effects of J and the crystal field splittings on the charge distribution between the bands.
Orbital differentiation in Hund metals
Physical Review B
Orbital differentiation is a common theme in multi-orbital systems, yet a complete understanding of it is still missing. Here, we consider a minimal model for orbital differentiation in Hund metals with a highly accurate method: We use the numerical renormalization group as real-frequency impurity solver for a dynamical mean-field study of three-orbital Hubbard models, where a crystal field shifts one orbital in energy. The individual phases are characterized with dynamic correlation functions and their relation to diverse Kondo temperatures. Upon approaching the orbital-selective Mott transition, we find a strongly suppressed spin coherence scale and uncover the emergence of a singular Fermi liquid and interband doublon-holon excitations. Our theory describes the diverse polarization-driven phenomena in the t2g bands of materials such as ruthenates and iron-based superconductors, and our methodological advances pave the way towards real-frequency analyses of strongly correlated materials.
Chinese Physics B, 2010
An impurity solver for the dynamical mean field (DMFT) study of the Mott insulators is proposed, which is based on the second order perturbation of the hybridization function. After carefully benchmarking it with Quantum Monte Carlo results on the anti-ferromagnetic phase of the Hubbard model, we conclude that this impurity solver can capture the main physical features in the strong coupling regime and can be a very useful tool for the LDA+DMFT studies of the Mott insulators with long range order.
Journal of Physics: Condensed Matter, 2021
We study the ground state phase diagram of the degenerate two-band Hubbard model at integer fillings as a function of onsite Hubbard interaction U and Hund’s exchange coupling J. We use a variational slave-spin mean field method which allows symmetry broken states to be studied within the computationally less intensive slave-spin mean field formalism. The results show that at half-filling, the ground state at smaller U is a Slater antiferromagnet with substantial local charge fluctuations. As U is increased, the antiferromagnetic (AF) state develops a Heisenberg behavior, finally undergoing a first-order transition to a Mott insulating AF state at a critical interaction U c which is of the order of the bandwidth. Introducing the Hund’s coupling J correlates the system more and reduces U c drastically. At quarter-filling with one electron per site, the ground state at smaller U is paramagnetic metallic. At finite J, as interaction is increased beyond a lower critical value U c1, it g...
Physica B: Condensed Matter, 2006
Using a local moment approach of Logan et al. we developed a solver for a multi-orbital single impurity Anderson model. The existence of the local moments is taken from the outset and their values are determined through variational principle by minimizing the corresponding ground state energy. The method is used to solve the dynamical mean-field equations for the multi-orbital Hubbard model. In particular, the Mott-Hubbard metal-insulator transition is addressed within this approach.
Local moment approach as a quantum impurity solver for the Hubbard model
Physical Review B, 2016
The local moment approach (LMA) has presented itself as a powerful semi-analytical quantum impurity solver (QIS) in the context of the dynamical mean-field theory (DMFT) for the periodic Anderson model and it correctly captures the low energy Kondo scale for the single impurity model, having excellent agreement with the Bethe ansatz and numerical renormalization group results. However, the most common correlated lattice model, the Hubbard model, has not been explored well within the LMA+DMFT framework beyond the insulating phase. Here in our work, within the framework we attempt to complete the phase diagram of the single band Hubbard model at zero temperature. Our formalism is generic to any particle filling and can be extended to finite temperature. We contrast our results with another QIS, namely the iterated perturbation theory (IPT) and show that the second spectral moment sum-rule improves better as the Hubbard interaction strength grows stronger in LMA, whereas it severely breaks down after the Mott transition in IPT. We also show that, in the metallic phase, the low-energy scaling of the spectral density leads to universality which extends to infinite frequency range at infinite correlation strength (strong-coupling). At large interaction strength, the off half-filling spectral density forms a pseudogap near the Fermi level and filling-controlled Mott transition occurs as one approaches the half-filling. Finally we study optical properties and find universal features such as absorption peak position governed by the low-energy scale and a doping independent crossing point, often dubbed as the isosbestic point in experiments.