Finite-temperature Exact Diagonalization Research Articles

Smooth Self-energy in the Exact-diagonalization-based Dynamical Mean-field Theory: Intermediate-representation Filtering Approach

We propose a method for estimating smooth real-frequency self-energy in the dynamical mean-field theory with the finite-temperature exact diagonalization (DMFT-ED). One of the benefits of DMFT-ED calculations is that one can obtain real-frequency spectra without a numerical analytic continuation. However, these spectra are spiky and strongly depend on the way to discretize a continuous bath (e.g., the number of the bath sites). The present scheme is based on a recently proposed compact representation of imaginary-time Green's functions, the intermediate representation (IR). The projection onto the IR basis acts as a noise filter for the discretization errors in the self-energy. This enables to extract the physically relevant part from the noisy self-energy. We demonstrate the method for single-site DMFT calculations of the single-band Hubbard model. We also show the results can be further improved by numerical analytic continuation.

Classical and quantum spin dynamics of the honeycomb Γ model

Quantum to classical crossover is a fundamental question in dynamics of quantum many-body systems. In frustrated magnets, for example, it is highly non-trivial to describe the crossover from the classical spin liquid with a macroscopically-degenerate ground-state manifold, to the quantum spin liquid phase with fractionalized excitations. This is an important issue as we often encounter the demand for a sharp distinction between the classical and quantum spin liquid behaviors in real materials. Here we take the example of the classical spin liquid in a frustrated magnet with novel bond-dependent interactions to investigate the classical dynamics, and critically compare it with quantum dynamics in the same system. In particular, we focus on signatures in the dynamical spin structure factor. Combining Landau-Lifshitz dynamics simulations and the analytical Martin-Siggia-Rose (MSR) approach, we show that the low energy spectra are described by relaxational dynamics and highly constrained by the zero mode structure of the underlying degenerate classical manifold. Further, the higher energy spectra can be explained by precessional dynamics. Surprisingly, many of these features can also be seen in the dynamical structure factor in the quantum model studied by finite-temperature exact diagonalization. We discuss the implications of these results, and their connection to recent experiments on frustrated magnets with strong spin-orbit coupling.

Valence fluctuations and empty-state resonance for Fe adatom on a surface

We report on the formation of the high-energy empty-state resonance in the electronic spectrum of the iron adatom on the Pt(111) surface. By using the combination of the first-principles methods and the finite-temperature exact diagonalization approach, we show that the resonance is the result of the valence fluctuations between atomic configurations of the impurity. Our theoretical finding is fully confirmed by the results of the scanning tunneling microscopy measurements [M. F. Crommie et al., Phys. Rev. B 48, 2851 (1993)]. In contrast to the previous theoretical results obtained by using local spin density approximation, the paramagnetic state of the impurity in the experiment is naturally reproduced within our approach. This opens a way for interpretation of STM data collected earlier for metallic surface nanosystems with iron impurities.

Correlation effects in insulating surface nanostructures

We study the role of static and dynamical Coulomb correlation effects on the electronic and magnetic properties of individual Mn, Fe and Co adatoms deposited on the CuN surface. For these purposes, we construct a realistic Anderson model, solve it by using finite-temperature exact diagonalization method and compare the calculated one-particle spectral functions with the LDA+$U$ densities of states. In contrast to Mn/CuN and Fe/CuN, the cobalt system tends to form the electronic excitations at the Fermi level. Based on the calculated magnetic response functions, the relative relaxation times for the magnetic moments of impurity orbitals are estimated. To study the effect of the dynamical correlations on the exchange interaction in nanoclusters, we solve the two-impurity Anderson model for the Mn dimer on the CuN surface. It is found that the experimental exchange interaction can be well reproduced by employing $U$=3 eV, which is two times smaller than the value used in static mean-field LDA+$U$ calculations. This suggests on important role of dynamical correlations in the interaction between adatoms on a surface.

Correlated Dirac fermions on the honeycomb lattice studied within cluster dynamical mean field theory

The role of non-local Coulomb correlations in the honeycomb lattice is investigated within cluster dynamical mean field theory combined with finite-temperature exact diagonalization. The paramagnetic semi-metal to insulator transition is found to be in excellent agreement with finite-size determinantal Quantum Monte Carlo simulations and with cluster dynamical mean field calculations based on the continuous-time Quantum Monte Carlo approach. As expected, the critical Coulomb energy is much lower than within a local or single-site formulation. Short-range correlations are shown to give rise to a pseudogap and concomitant non-Fermi-liquid behavior within a narrow range below the Mott transition.

Correlation-induced spin freezing transition in FeSe: A dynamical mean field study

The effect of local Coulomb interactions on the electronic properties of FeSe is explored within dynamical mean field theory combined with finite-temperature exact diagonalization. The low-energy scattering rate is shown to exhibit non-Fermi-liquid behavior caused by the formation of local moments. Fermi-liquid properties are restored at large electron doping. In contrast, FeAsLaO is shown to be located on the Fermi-liquid side of this spin freezing transition.

Spectral weight of doping-induced states in the two-dimensional Hubbard model

The spectral weight of states induced in the Mott gap via hole doping in the two-dimensional Hubbard model is studied within cluster dynamical mean field theory combined with finite-temperature exact diagonalization. If the cutoff energy is chosen to lie just below the upper Hubbard band, the integrated weight per spin is shown to satisfy $W_+(\delta)\ge\delta$ ($\delta$ denotes the total number of holes), in agreement with model predictions by Eskes {\it et al.} [Phys. Rev. Lett. {\bf 67}, 1035 (1991)]. However, if the cutoff energy is chosen to lie in the range of the pseudogap, $W_+(\delta)$ remains much smaller than $\delta$ and approximately saturates near $\delta\approx 0.2...0.3$. The analysis of recent X-ray absorption spectroscopy data therefore depends crucially on the appropriate definition of the integration window.

Finite-temperature exact diagonalization cluster dynamical mean-field study of the two-dimensional Hubbard model: Pseudogap, non-Fermi-liquid behavior, and particle-hole asymmetry

The effect of doping in the two-dimensional Hubbard model is studied within finite-temperature exact diagonalization combined with cluster dynamical mean-field theory. By employing a mixed basis involving cluster sites and bath molecular orbitals for the projection of the lattice Green's function onto $2\ifmmode\times\else\texttimes\fi{}2$ clusters, a considerably more accurate description of the low-frequency properties of the self-energy is achieved than in a pure site picture. To evaluate the phase diagram, the transition from Fermi-liquid to non-Fermi-liquid behavior for decreasing hole doping is studied as a function of Coulomb energy, next-nearest-neighbor hopping, and temperature. The self-energy component ${\ensuremath{\Sigma}}_{X}$ associated with $X=(\ensuremath{\pi},0)$ is shown to develop a collective mode above ${E}_{F}$, whose energy and strength exhibits a distinct dispersion with doping. This low-energy excitation gives rise to non-Fermi-liquid behavior as the hole doping decreases below a critical value ${\ensuremath{\delta}}_{c}$, and to an increasing particle-hole asymmetry, in agreement with recent photoemission data. This behavior is consistent with the removal of spectral weight from electron states above ${E}_{F}$ and the opening of a pseudogap, which increases with decreasing doping. The phase diagram reveals that ${\ensuremath{\delta}}_{c}\ensuremath{\approx}0.15\dots{}0.20$ for various system parameters. For electron doping, the collective mode of ${\ensuremath{\Sigma}}_{X}(\ensuremath{\omega})$ and the concomitant pseudogap are located below the Fermi energy, which is consistent with the removal of spectral weight from the hole states just below ${E}_{F}$. The critical doping, which marks the onset of non-Fermi-liquid behavior, is systematically smaller than for hole doping.

Multisite versus multiorbital Coulomb correlations studied within finite-temperature exact diagonalization dynamical mean-field theory

The influence of short-range Coulomb correlations on the Mott transition in the single-band Hubbard model at half filling is studied within cellular dynamical mean-field theory for square and triangular lattices. Finite-temperature exact diagonalization is used to investigate correlations within two-, three-, and four-site clusters. Transforming the nonlocal self-energy from a site basis to a molecular-orbital basis, we focus on the interorbital charge transfer between these cluster molecular orbitals in the vicinity of the Mott transition. In all cases studied, the charge transfer is found to be small, indicating weak Coulomb-induced orbital polarization despite sizable level splitting between orbitals. These results demonstrate that all cluster molecular orbitals take part in the Mott transition and that the insulating gap opens simultaneously across the entire Fermi surface. Thus, at half filling we do not find orbital-selective Mott transitions or a combination of band filling and Mott transition in different orbitals. Nevertheless, the approach toward the transition differs greatly between cluster orbitals, giving rise to a pronounced momentum variation along the Fermi surface, in agreement with previous works. The near absence of Coulomb-induced orbital polarization in these clusters differs qualitatively from single-site multiorbital studies of several transition-metal oxides, where the Mott phase exhibits nearly complete orbital polarization as a result of a correlation driven enhancement of the crystal-field splitting. The strong single-particle coupling among cluster orbitals in the single-band case is identified as the source of this difference.

Exact diagonalization dynamical mean-field theory for multiband materials: Effect of Coulomb correlations on the Fermi surface ofNa0.3CoO2

Dynamical mean field theory combined with finite-temperature exact diagonalization is shown to be a suitable method to study local Coulomb correlations in realistic multi-band materials. By making use of the sparseness of the impurity Hamiltonian, exact eigenstates can be evaluated for significantly larger clusters than in schemes based on full diagonalization. Since finite-size effects are greatly reduced this approach allows the study of three-band systems down to very low temperatures, for strong local Coulomb interactions and full Hund exchange. It is also shown that exact diagonalization yields smooth subband quasi-particle spectra and self-energies at real frequencies. As a first application the correlation induced charge transfer between t2g bands in Na_0.3CoO_2 is investigated. For both Hund and Ising exchange the small eg' Fermi surface hole pockets are found to be slightly enlarged compared to the non-interacting limit, in agreement with previous Quantum Monte Carlo dynamical mean field calculations for Ising exchange, but in conflict with photoemission data.

Non-Fermi-liquid phases in the two-band Hubbard model: finite-temperature exact diagonalization study of Hund's rule coupling

The two-band Hubbard model involving subbands of different widths is investigated via finite-temperature exact diagonalization (ED) and dynamical mean field theory (DMFT). In contrast to the quantum Monte Carlo (QMC) method which at low temperatures includes only Ising-like exchange interactions to avoid sign problems, ED permits a treatment of Hund's exchange and other onsite Coulomb interactions on the same footing. The role of finite-size effects caused by the limited number of bath levels in this scheme is studied by analyzing the low-frequency behavior of the subband self-energies as a function of temperature, and by comparing with numerical renormalization group (NRG) results for an effective one-band model. For half-filled, non-hybridizing bands, the metallic and insulating phases are separated by an intermediate mixed phase with an insulating narrow and a bad-metallic wide subband. The wide band in this phase exhibits different degrees of non-Fermi-liquid behavior, depending on the treatment of exchange interactions. Whereas for complete Hund's coupling, infinite lifetime is found at the Fermi level, in the absence of spin-flip and pair-exchange, this lifetime becomes finite. Excellent agreement is obtained both with new NRG and previous QMC/DMFT calculations. These results suggest that-finite temperature ED/DMFT might be a useful scheme for realistic multi-band materials.