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arXiv:2107.06517 · Physical review. B./Physical review. B

Natural orbital impurity solver for real-frequency properties at finite temperature

Motoharu Kitatani, 志朗 酒井, Ryotaro Arita

Published Nov 13, 2023• 1 citation
arXivHTMLPDF

Abstract

We extend the natural orbital impurity solver [Y. Lu, M. H\"oppner, O. Gunnarsson, and M. W. Haverkort, Phys. Rev. B 90, 085102 (2014)] to finite temperatures and apply it to calculate spectral and transport properties of correlated electrons within the dynamical mean-field theory. First, we benchmark our method against the exact diagonalization result for small clusters, finding that the natural orbital scheme works well not only for zero temperature but for low finite temperatures. The method yields smooth and sufficiently accurate spectra, which agree well with the results of the numerical renormalization group. Using the smooth spectra, we calculate the electric conductivity and Seebeck coefficient for the two-dimensional Hubbard model at low temperatures which are within the scope of many experiments and practical applications. These results demonstrate the usefulness of the natural orbital framework for obtaining the real frequency information of correlated electron systems.

DOI
10.1103/physrevb.108.195124

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We extend the natural orbital impurity solver [Y. Lu, M. H"oppner, O. Gunnarsson, and M. W. Haverkort, Phys. Rev. B 90, 085102 (2014)] to finite temperatures and apply it to calculate spectral and transport properties of correlated electrons within the dynamical mean-field theory. First, we benchmark our method against the exact diagonalization result for small clusters, finding that the natural orbital scheme works well not only for zero temperature but for low finite temperatures. The method yields smooth and sufficiently accurate spectra, which agree well with the results of the numerical renormalization group. Using the smooth spectra, we calculate the electric conductivity and Seebeck coefficient for the two-dimensional Hubbard model at low temperatures which are within the scope of many experiments and practical applications. These results demonstrate the usefulness of the natural orbital framework for obtaining the real frequency information of correlated electron systems.
The natural orbitals renormalization group (NORG) has previously been proposed as an efficient numerical method for solving zero-temperature properties of multisite and multiorbital quantum impurity systems. Here, we implement the NORG as an impurity solver for dynamical mean-field theory (DMFT). In comparison with the exact diagonalization method, the NORG method can treat much more bath sites in an impurity model to which the DMFT maps a lattice model and can find accurate zero-temperature Matsubara and low-frequency retarded Green's functions. We demonstrate the effectiveness of this method on a two-orbital Hubbard model on the Bethe lattice and find successfully the orbital selective Mott transition with a Kondo resonance peak in the wide band and two holon-doublon bound state excitation peaks in the narrow band.
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We here present how a self-consistent solution of the dynamical mean field theory equations can be obtained using exact diagonalization of an Anderson impurity model with accuracies comparable to those found using renormalization group or quantum Monte Carlo methods. We show how one can solve a correlated quantum impurity coupled to several hundred uncorrelated bath sites, using a restricted active basis set. The number of bath sites determines the resolution of the obtained spectral function, which consists of peaks roughly spaced by the band width divided by the number of bath sites. The self-consistency cycles are fully performed on the real frequency axis and expressed as numerical stable matrix operations. The same impurity solver has been used on Ligand Field and finite size cluster calculations and is capable of treating involved Hamiltonians including the full rotational invariant Coulomb interaction, spin-orbit coupling and low symmetry crystal-fields. The proposed method allows for the calculation of a variety of correlation functions at little extra cost.
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One of the most important and accurate approaches for studying interacting many-electron correlated systems is the quantum renormalization group (RG) procedure, upon which we propose a concept in the framework of natural orbitals so that we can generalize the RG into general orbital space. To demonstrate its effectiveness, we apply this new approach on a quantum cluster-impurity model with four impurities in comparison with the exact diagonalization method. We also find a shortcut to dramatically improving this RG procedure. A profound impact on the cluster dynamical mean-field theory and multi-impurity/orbital Kondo problems is further discussed.
Wilson's numerical renormalization group method for the calculation of dynamic properties of impurity models is generalized to investigate the effective impurity model of the dynamical mean-field theory at finite temperatures. We calculate the spectral function and self-energy for the Hubbard model on a Bethe lattice with infinite coordination number directly on the real-frequency axis and investigate the phase diagram for the Mott-Hubbard metal-insulator transition. While for $T<{T}_{\mathrm{c}}\ensuremath{\approx}0.02W$ (W:(W:(W: bandwidth) we find hysteresis with first-order transitions both at Uc1{U}_{\mathrm{c}1}Uc1​ (defining the insulator to metal transition) and at Uc2{U}_{\mathrm{c}2}Uc2​ (defining the metal to insulator transition), at T>TcT>{T}_{\mathrm{c}}T>Tc​ there is a smooth crossover from metalliclike to insulatinglike solutions.