Single-site Dynamical Mean-field Theory Research Articles

Optical conductivity of the two-dimensional Hubbard model: Vertex corrections, emergent Galilean invariance, and the accuracy of the single-site dynamical mean field approximation

We compute the frequency-dependent conductivity of the two-dimensional square lattice Hubbard model at zero temperature as a function of density to second order in the interaction strength, and compare the results to the predictions of single-site dynamical mean field theory computed at the same order. We find that despite the neglect of vertex corrections, the single-site dynamical mean field approximation produces semiquantitatively accurate results for most carrier concentrations, but fails qualitatively for the nearly empty or nearly filled band cases where the model exhibits an emergent Galilean invariance. The DMFT approximation also becomes qualitatively inaccurate very near half filling if nesting is important.

Is the Orbital-Selective Mott Phase Stable against Interorbital Hopping?

The localization-delocalization transition is at the heart of strong correlation physics. Recently, there is great interest in multiorbital systems where this transition can be restricted to certain orbitals, leading to an orbital-selective Mott phase (OSMP). Theoretically, the OSMP is widely studied for kinetically decoupled orbitals, but the effect of interorbital hopping remains unclear. Here, we show how nonlocal interorbital hopping leads to local hybridization in single-site dynamical mean-field theory (DMFT). Under fairly general circumstances, this implies that, at zero temperature, the OSMP, involving the Mott-insulating state of one orbital, is unstable against interorbital hopping to a different, metallic orbital. We further show that the coherence scale below which all electrons are itinerant is very small and gets exponentially suppressed even if the interorbital hopping is not overly small. Within this framework, the OSMP with interorbital hopping may thus reach down to extremely low temperatures T, but not to T=0. Accordingly, it is part of a coherence-incoherence crossover and not a quantum critical point. We present analytical arguments supported by numerical results using the numerical renormalization group as a DMFT impurity solver. We also compare our findings with previous slave-spin studies.

Development of an efficient impurity solver in dynamical mean field theory for multiband systems: Iterative perturbation theory combined with parquet equations

Although several impurity solvers in the dynamical mean field theory (DMFT) have been proposed, especially in multi-band systems, there are practical difficulties arising from a trade-off between numerical costs and reliability. In this study, we re-interpret the iterative perturbation theory (IPT) as an approximation which captures the strong correlation effects by mimicking the particular frequency structures of the exact full vertex, and extend it such that it can have efficiency and reliability simultaneously by modifying IPT vertex using the parquet equations. We apply this method to several models to evaluate their validity. We confirm that our method shows good agreements with the numerically exact continuous-time quantum Monte Carlo method in the single-site DMFT calculation.

Electronic correlations in the normal state of the kagome superconductor KV3Sb5

Recently, intensive studies have revealed fascinating physics, such as charge density wave and superconducting states, in the newly synthesized kagome-lattice materials ${A\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ $(A=\text{K}, \mathrm{Rb}, \mathrm{Cs})$. Despite the rapid progress, fundamental aspects such as the magnetic properties and electronic correlations in these materials have not been clearly understood yet. Here, based on density functional theory plus single-site dynamical mean-field theory calculations, we investigate the correlated electronic structure and magnetic properties of the ${\mathrm{KV}}_{3}{\mathrm{Sb}}_{5}$ family materials in the normal state. We show that these materials are good metals with weak local correlations. The obtained Pauli-like paramagnetism and the absence of local moments are consistent with a recent experiment. We reveal that the band crossings around the Fermi level form three groups of nodal lines protected by the spacetime inversion symmetry, each carrying a quantized $\ensuremath{\pi}$ Berry phase. Our result suggests that the local correlation strength in these materials appears to be too weak to generate unconventional superconductivity, and nonlocal electronic correlation might be crucial in this kagome system.

Protracted Kondo screening and kagome bands in the heavy-fermion metal Ce3Al

Ce$_{3}$Al is an archetypal heavy-fermion compound with multiple crystalline phases. Here, we try to investigate its electronic structures in the hexagonal phase ($\alpha$-Ce$_{3}$Al) and cubic phase ($\beta$-Ce$_{3}$Al) by means of a combination of density functional theory and single-site dynamical mean-field theory. We confirm that the 4$f$ valence electrons in both phases are itinerant, accompanied with strong valence state fluctuations. Their 4$f$ band structures are heavily renormalized by electronic correlations, resulting in large effective electron masses. The Kondo screening in Ce$_{3}$Al would be protracted over a wide range of temperature since the single-impurity Kondo temperature $T_{K}$ is much higher than the coherent Kondo temperature $T^{*}_{K}$. Especially, the crystal structure of $\alpha$-Ce$_{3}$Al forms a layered kagome lattice. We observe conspicuous kagome-derived flat bands and Dirac cones (or gaps) in its quasiparticle band structure. Therefore, it is concluded that the hexagonal phase of Ce$_{3}$Al will be a promising candidate of heavy-fermion kagome metal.

Slope invariant T -linear resistivity from local self-energy

A theoretical understanding of the enigmatic linear-in-temperature (T) resistivity, ubiquitous in strongly correlated metallic systems, has been a long sought-after goal. Furthermore, the slope of this robust T-linear resistivity is also observed to stay constant through crossovers between different temperature regimes: a phenomenon we dub “slope invariance.” Recently, several solvable models with T-linear resistivity have been proposed, putting us in an opportune moment to compare their inner workings in various explicit calculations. We consider two strongly correlated models with local self-energies that demonstrate T linearity: a lattice of coupled Sachdev-Ye-Kitaev models and the Hubbard model in single-site dynamical mean-field theory. We find that the two models achieve T linearity through distinct mechanisms at intermediate temperatures. However, we also find that these mechanisms converge to an identical form at high temperatures. Surprisingly, both models exhibit “slope invariance” across the two temperature regimes. Thus not only do we reveal some of the diversity in the theoretical inner workings that can lead to T-linear resistivity, but we also establish that different mechanisms can result in “slope invarance.”Received 28 October 2019Revised 10 July 2020Accepted 16 July 2020Corrected 11 December 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.033434Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectrical conductivityPhysical SystemsStrongly correlated systemsTechniquesDynamical mean field theoryHubbard modelNon-Fermi-liquid theorySachdev-Ye-Kitaev modelCondensed Matter & Materials Physics

Unraveling the 4f electronic structures of cerium monopnictides

We employed a state-of-the-art first-principles many-body approach, namely the density functional theory in combination with the single-site dynamical mean-field theory, to study the 4f electronic structures in cerium monopnictides (CeX, where X = N, P, As, Sb, and Bi). We find that the 4f electrons in CeN are highly itinerant and mixed-valence, showing a prominent quasiparticle peak near the Fermi level. On the contrary, they become well localized and display weak valence fluctuation in CeBi. It means that a 4f itinerant-localized crossover could emerge upon changing the X atom from N to Bi. Moreover, according to the low-energy behaviors of 4f self-energy functions, we could conclude that the 4f electrons in CeX also demonstrate interesting orbital-selective electronic correlations, which are similar to the other cerium-based heavy fermion compounds.

Interaction and temperature effects on the magneto-optical conductivity of Weyl liquids

Negative magnetoresistance is one of the manifestations of the chiral anomaly in Weyl semimetals. The magneto-optical conductivity also shows transitions between Landau levels that are not spaced as in an ordinary electron gas. How are such topological properties modified by interactions and temperature? We answer this question by studying a lattice model of Weyl semimetals with an on-site Hubbard interaction. Such an interacting Weyl semimetal, dubbed as Weyl liquid, may be realized in Mn$_3$Sn. We solve that model with single-site dynamical mean-field theory. We find that in a Weyl liquid, quasiparticles can be characterized by a quasiparticle spectral weight $Z$, although their lifetime increases much more rapidly as frequency approaches zero than in an ordinary Fermi liquid. The negative magnetoresistance still exists, even though the slope of the linear dependence of the DC conductivity with respect to the magnetic filed is decreased by the interaction. At elevated temperatures, a Weyl liquid crossesover to bad metallic behavior where the Drude peak becomes flat and featureless.

Electronic structure evolution accompanying heavy fermion formation in CeCu2Si2

The cooper pairs in the heavy-fermion superconductor CeCu2Si2 are formed of heavy fermions. Therefore, the heavy fermions are fundamental to the emergence of unconventional superconductivity and associated non-Fermi-liquid behavior in the normal state. The interplay between localization and itinerancy manifested on the electronic structure is key for understanding the heavy-fermion behavior. Here, via the first-principle density functional theory (DFT) combined with single-site dynamical mean-field theory (DMFT), we investigate the temperature ( T ) evolution of the electronic structure of CeCu2Si2 in the normal state, focusing on the role of the 4 f states in the low energy regime. Two characteristic temperature scales of this evolution, which accompanied the heavy-fermion formation, are established. The coherence onset temperature is around 130 K, whereas the heavy-fermion band formation temperature is between 40 and 80 K; both characteristic temperature scales are higher than the transport coherence temperature. Furthermore, the heavy-fermion formation is confirmed by calculating its effective mass variation with the temperature. Based on the calculated T- dependent evolution of the 4 f orbital occupancy and electronic structure, an explanation on the behavior of the temperature evolution of the correlation strength of CeCu2Si2 is provided. Our results offer a comprehensive microscopic picture of the heavy-fermion formation in CeCu2Si2, which is essential for further understanding the emergent superconducting pairing mechanism.

Emergence of quasiparticle multiplets in curium

A combination of the density functional theory and the single-site dynamical mean-field theory is employed to study the electronic structures of various allotropes of elemental curium (Cm-I, Cm-II, and Cm-III). We find that the 5$f$ valence electrons in the high-symmetry Cm-I and Cm-II phases remain localized, while they turn into itinerancy in the low-symmetry monoclinic Cm-III phase. In addition, conspicuous quasiparticle multiplets are identified in the 5$f$ electronic density of states of the Cm-III phase. We believe that it is the many-body transition between $5f^{7}$ and $5f^{8}$ configurations that gives rise to these quasiparticle multiplets. Therefore, the Cm-III phase is probably a new realization of the so-called Racah metal.

Continuous momentum dependence in the dynamical cluster approximation

The dynamical cluster approximation (DCA) is a quantum cluster extension to the single-site dynamical mean-field theory that incorporates spatially nonlocal dynamic correlations systematically and nonperturbatively. The DCA$^+$ algorithm addresses the cluster shape dependence of the DCA and improves the convergence with cluster size by introducing a lattice self-energy with continuous momentum dependence. However, we show that the DCA$^+$ algorithm is plagued by a fundamental problem when its self-consistency equations are formulated using the bare Green's function of the cluster. This problem is most severe in the strongly correlated regime at low doping, where the DCA$^+$ self-energy becomes overly metallic and local, and persists to cluster sizes where the standard DCA has long converged. In view of the failure of the DCA$^+$ algorithm, we propose to complement DCA simulations with a post-interpolation procedure for single-particle and two-particle correlation functions to preserve continuous momentum dependence and the associated benefits in the DCA. We demonstrate the effectiveness of this practical approach with results for the half-filled and hole-doped two-dimensional Hubbard model.

Exploring the exotic f states of prototype compounds CeSb and USb

To unravel the interplay between the strong electronic correlation and itinerant-localized dual nature in typical f electron systems, we employed the density functional theory in combination with the single-site dynamical mean-field theory to systematically investigate the electronic structures of CeSb and USb. We find that the 4f states in CeSb are mostly localized with a weak quasi-particle resonance peak near the Fermi level. Conversely, the 5f electrons in USb display partially itinerant features, accompanied by mixed-valence behavior and prominent valence state fluctuations. Particularly, the 4f electronic correlations in CeSb are orbital-selective with strikingly renormalized 4f5/2 states, according to the low-energy behaviors of 4f self-energy functions. It is believed that the strong electronic correlation and fantastic bonding of f states contribute to elucidating the magnetism.

Nature of the 5f electronic structure of plutonium

Plutonium (Pu), in which the 5$f$ valence electrons always wander the boundary between localized and itinerant states, exhibits quite complex crystal structures and unprecedentedly anomalous properties with respect to temperature and alloying. Understanding its chemical and physical properties, especially its 5$f$ electronic structure is one of the central and unsolved topics in condensed matter theory. In the present work, the electronic structures of the six allotropes of Pu (including its $\alpha$, $\beta$, $\gamma$, $\delta$, $\delta'$, and $\epsilon$ phases) at ambient pressure are studied comprehensively by means of the density functional theory in combination with the single-site dynamical mean-field theory. The band structures, total and partial density of states, valence state histograms, 5$f$ orbital occupancies, X-ray branching ratios, and self-energy functions are carefully studied. It is suggested that the $\alpha$, $\beta$, and $\gamma$ phases of Pu are typical Racah metals in which the atomic multiple effect dominates near the Fermi level. The calculated results reveal that not only the $\delta$ phase, but also all the six allotropes are archetypal mixed-valence metals with remarkable atomic eigenstate fluctuation. In consequence of that, the 5$f$ occupancy $n_{5f}$ is around 5.1 $\sim$ 5.4, which varies with respect to the atomic volume and electronic correlation strength of Pu. The 5$f$ electronic correlation in Pu is moderately orbital-dependent. Moreover, the 5$f$ electrons in the $\delta'$ phase are the most correlated and localized.

High-Resolution Photoemission on Sr2RuO4 Reveals Correlation-Enhanced Effective Spin-Orbit Coupling and Dominantly Local Self-Energies

We explore the interplay of electron-electron correlations and spin-orbit coupling in the model Fermi liquid Sr2RuO4 using laser-based angle-resolved photoemission spectroscopy. Our precise measurement of the Fermi surface confirms the importance of spin-orbit coupling in this material and reveals that its effective value is enhanced by a factor of about two, due to electronic correlations. The self-energies for the $\beta$ and $\gamma$ sheets are found to display significant angular dependence. By taking into account the multi-orbital composition of quasiparticle states, we determine self-energies associated with each orbital component directly from the experimental data. This analysis demonstrates that the perceived angular dependence does not imply momentum-dependent many-body effects, but arises from a substantial orbital mixing induced by spin-orbit coupling. A comparison to single-site dynamical mean-field theory further supports the notion of dominantly local orbital self-energies, and provides strong evidence for an electronic origin of the observed non-linear frequency dependence of the self-energies, leading to `kinks' in the quasiparticle dispersion of Sr2RuO4.

Parquet approximation for molecules: Spectrum and optical conductivity of the Pariser-Parr-Pople model

We study a simple model system for the conjugated $\pi$-bonds in benzene, the Pariser-Parr-Pople (PPP) model, within the parquet approximation (PA), exemplifying the prospects of the PA for molecules. Advantages of the PA are the polynomial scaling with the number of orbitals, and the natural calculation of one- and two-particle spectral functions as well as of response and correlation functions. We find large differences in the electronic correlations in the PPP model compared to a Hubbard model with only local interactions. The quasiparticle renormalization (or mass enhancement) is much weaker in the PPP than in the Hubbard model, but the static part of the self-energy enhances the band gap of the former. Furthermore, the vertex corrections to the optical conductivity are much more important in the PPP model. Because non-local interactions strongly alter the self-energy, we conclude that the PA is more suitable for calculating conjugated $\pi$-bonds in molecules than single site dynamical mean-field theory.

Electronic structure of cerium: A comprehensive first-principles study

Cerium, in which the 4$f$ valence electrons live at the brink between localized and itinerant characters, exhibits varying crystal structures and therefore anomalous physical properties with respect to temperature and pressure. Understanding its electronic structure and related lattice properties is one of the central topics in condensed matter theory. In the present work, we employed the state-of-the-art first-principles many-body approach (i.e., the density functional theory in combination with the single-site dynamical mean-field theory) to study its electronic structure thoroughly. The momentum-resolved spectral functions, total and $4f$ partial density of states, optical conductivities, self-energy functions, and atomic eigenstate histograms for cerium's four allotropes under ambient pressure were calculated and analyzed carefully. The calculated results demonstrate that the 4$f$ electrons in the $\alpha$, $\beta$, $\gamma$, and $\delta$ phases are all correlated with heavily remormalized electron masses. In the $\alpha$ phase, the 4$f$ electrons tend to be itinerant, which cause strong hybridization between the 4$f$ and $spd$ bands and remarkable 4$f$ valence state fluctuation. While for the other phases, the 4$f$ electrons are close to be localized. Our calculated results support the Kondo volume collapse scenario for the cerium $\alpha-\gamma$ transition. Finally, we examined the site dependence of $4f$ electronic structure in the $\beta$ phase. The calculated results suggest that it doesn't exhibit a site selective 4$f$ localized state, contrary to previous prediction.

Pressure-driven 5f localized-itinerant transition and valence fluctuation in cubic phase californium

A combination of the density functional theory and the single-site dynamical mean-field theory is employed to study the pressure dependence of electronic structure for cubic phase californium. We predict that its 5$f$ electrons could undergo an orbital-selective localized-itinerant transition under moderate pressure. The volume contraction causes remarkable charge redistribution and valence fluctuation behaviors, which are the driving forces of the divalent-trivalent transition. Additionally, we find that the angular momentum coupling mechanism is hardly affected by pressure. The 5$f$ orbital occupancy is well described by the intermediate coupling scheme.

Improved Hubbard-I approximation impurity solver for quantum impurity models

We develop a fast impurity solver which is based on the combination of Hubbard-I approximation and hybridization expansion continuous-time quantum Monte Carlo algorithm. This solver inherits the advantages of both algorithms. In order to demonstrate the power and usefulness of this solver, we use it to study the magnetic phase transitions of single-band and two-band Hubbard models in the framework of single-site dynamical mean-field theory. The calculated results agree well with those obtained by hybridization expansion quantum impurity solver. It is suggested that this solver is very suitable to solve the multi-orbital quantum impurity models efficiently and can be used to study more realistic systems with magnetic long-range order in the future.

Itinerant-localized crossover and orbital dependent correlations for 4f electrons in cerium-based ternary 122 compounds

The electronic structures of cerium-based ternary 122 compounds Ce$M_{2}$Si$_{2}$, where $M =$ Ru, Rh, Pd, and Ag, are investigated systematically by using the density functional theory in combination with the single-site dynamical mean-field theory. The momentum-resolved spectral functions, total and 4$f$ partial density of states, self-energy functions, and valence state fluctuations are calculated. The obtained results are in good accord with the available experimental data. It is suggested that, upon increasing atomic number from Ru to Ag, the 4$f$ electrons should become increasingly localized. An itinerant-localized crossover for 4$f$ electrons driven by chemical pressure may emerge when $M$ changes from Pd to Ag. Particularly, according to the low-frequency behaviors of 4$f$ self-energy functions, we identify an orbital selective 4$f$ insulating state in CeAg$_{2}$Si$_{2}$, which is totally unexpected.

Hundness versus Mottness in a three-band Hubbard–Hund model: On the origin of strong correlations in Hund metals

Hund metals are multi-orbital systems with moderate Coulomb interaction, U, among charges and sizeable Hund’s rule coupling, J(<U), that aligns the spins in different orbitals. They show strong correlation effects, like very low Fermi-liquid coherence scales and intriguing incoherent transport regimes, resulting in bad metallic behavior. But to what extent are these strong correlations governed by Mottness, i.e. the blocking of charge fluctuations close to a Mott insulator transition (MIT) induced by U, or by Hundness, a new route towards strong correlations induced by J? To answer this question, we study the full phase diagram of a degenerate three-band Hubbard–Hund model on a Bethe lattice at zero temperature using single-site dynamical mean-field theory and the numerical renormalization group as efficient real-frequency multi-band impurity solver. Hund metal behavior occurs in this minimal model for a filling close to nd=2, moderate U and sizeable J, the “Hund-metal regime”. In particular, strong correlations manifest themselves there by an unusually low quasiparticle weight. Generalizing previous results on this model, we show that “spin–orbital separation” (SOS) is a generic Hund’s-coupling-induced feature in the whole metallic regime of the phase diagram for 1<nd<3 and sizeable J. There orbital screening always occurs at much higher energies than spin screening below which Fermi-liquid behavior sets in. The low quasiparticle weight can then be directly explained in terms of the Hund’s-coupling-reduced Fermi-liquid scale. We carefully analyze the effect of J (Hundness), and the effect of the MIT at nd=2 and nd=3 (Mottness) on the energy scales and the nature of SOS. In the Hund-metal regime, far from any MIT, Hundness is shown to be the key player to induce strong correlations by constraining the spin rather than the charge dynamics. There, physical properties are governed by a broad incoherent energy regime of SOS where intriguing Hund metal physics occurs: large, almost unscreened spins are coupled to screened orbital degrees of freedom. With increasing proximity to an MIT correlations are further enhanced and the Fermi-liquid scale is further reduced. However, in the Hund-metal regime, this effect of Mottness is minor. In contrast, very close to the MIT at nd=2, the incoherent spin–orbital separation regime is strongly downscaled and becomes negligibly small, whereas Mottness – the localization of charges – becomes dominant in inducing strong correlations. Close to the MIT at nd=3, the SOS regime widens up because the orbital degrees of freedom get blocked by the formation of an S=32 impurity spin, but its nature changes: the orbital and spin dynamics get decoupled. Our results confirm Hundness as a distinct mechanism towards strong correlations in the normal state of Hund metals, leading to various interesting implications for the nature of electronic transport.