One-particle Spectral Function Research Articles

Low-energy peak in the one-particle spectral function of the electron gas at metallic densities

Low-energy peak in the one-particle spectral function of the electron gas at metallic densities

Emergent normal-state Mottness in the infinite-layer NdNiO2 superconductor

We present a computational study based on density functional plus dynamical mean-field theory calculations for the normal-state electronic reconstruction of pure and hole-doped ${\mathrm{NdNiO}}_{2}$ superconductors. Our results capture the $T$ dependence of the electrical resistivity, providing a many-particle interpretation of the emergence of pseudogaplike features at low energies as well as the weakly insulating regime seen in experiment. We show how Mottness manifests itself in the weak localization to bad-metallicity crossover due to strong correlation in the ${e}_{g}$-shell one-particle spectral functions and self-energies.

Polarons in spinless metals—a variational solution

We propose a simple variational solution for calculating one-particle spectral functions in lattice models of spinless metals with strong electron-phonon coupling. It is based on a generalization of the Momentum Average variational approximation for single polarons, combined with the assumption that the other fermions in the system are locked into an inert Fermi sea. We expect the method to be accurate for fermion addition spectral functions in metals with a small Fermi energy (nearly empty band), and for fermion removal spectral functions in metals with a large Fermi energy (nearly full band), provided that the characteristic phonon frequency is not too small. Both these regions are far from the region where the Migdal theorem holds, thus our results offer new insights into polaronic behavior in a largely unexplored part of the parameter space. Here, we show results for the Holstein coupling in one-dimension and present ways to gauge their accuracy, but ultimately this will need to be verified against numerical calculations. This variational method can be extended straightforwardly to higher dimensions and other forms of electron-phonon coupling.

Magnetic Properties and Pseudogap Formation in Infinite-Layer Nickelates: Insights From the Single-Band Hubbard Model

We study the magnetic and spectral properties of a single-band Hubbard model for the infinite-layer nickelate compound LaNiO2. As spatial correlations turn out to be the key ingredient for understanding its physics, we use two complementary extensions of the dynamical mean-field theory to take them into account: the cellular dynamical mean-field theory and the dynamical vertex approximation. Additionally to the systematic analysis of the doping dependence of the non-Curie-Weiss behavior of the uniform magnetic susceptibility, we provide insight into its relation to the formation of a pseudogap regime by the calculation of the one-particle spectral function and the magnetic correlation length. The latter is of the order of a few lattice spacings when the pseudogap opens, indicating a strong-coupling pseudogap formation in analogy to cuprates.

Machine learning of Kondo physics using variational autoencoders and symbolic regression

We employ variational autoencoders to extract physical insight from a dataset of one-particle Anderson impurity model spectral functions. Autoencoders are trained to find a low-dimensional, latent space representation that faithfully characterizes each element of the training set, as measured by a reconstruction error. Variational autoencoders, a probabilistic generalization of standard autoencoders, further condition the learned latent space to promote highly interpretable features. In our study, we find that the learned latent variables strongly correlate with well known, but nontrivial, parameters that characterize emergent behaviors in the Anderson impurity model. In particular, one latent variable correlates with particle-hole asymmetry, while another is in near one-to-one correspondence with the Kondo temperature, a dynamically generated low-energy scale in the impurity model. Using symbolic regression, we model this variable as a function of the known bare physical input parameters and "rediscover" the non-perturbative formula for the Kondo temperature. The machine learning pipeline we develop suggests a general purpose approach which opens opportunities to discover new domain knowledge in other physical systems.

Tree tensor-network real-time multiorbital impurity solver: Spin-orbit coupling and correlation functions in Sr2RuO4

We present a tree tensor-network impurity solver suited for general multiorbital systems. The network is constructed to efficiently capture the entanglement structure and symmetry of an impurity problem. The solver works directly on the real-time/frequency axis and generates spectral functions with energy-independent resolution of the order of one percent of the correlated bandwidth. Combined with an optimized representation of the impurity bath, it efficiently solves self-consistent dynamical mean-field equations and calculates various dynamical correlation functions for systems with off-diagonal Green's functions. For the archetypal correlated Hund's metal Sr$_2$RuO$_4$, we show that both the low-energy quasiparticle spectra related to the van Hove singularity and the high-energy atomic multiplet excitations can be faithfully resolved. In particular, we show that while the spin-orbit coupling has only minor effects on the orbital-diagonal one-particle spectral functions, it has a more profound impact on the low-energy spin and orbital response functions.

A general charge transport picture for organic semiconductors with nonlocal electron-phonon couplings

The nonlocal electron-phonon couplings in organic semiconductors responsible for the fluctuation of intermolecular transfer integrals has been the center of interest recently. Several irreconcilable scenarios coexist for the description of the nonlocal electron-phonon coupling, such as phonon-assisted transport, transient localization, and band-like transport. Through a nearly exact numerical study for the carrier mobility of the Holstein-Peierls model using the matrix product states approach, we locate the phonon-assisted transport, transient localization and band-like regimes as a function of the transfer integral (V) and the nonlocal electron-phonon couplings (ΔV), and their distinct transport behaviors are analyzed by carrier mobility, mean free path, optical conductivity and one-particle spectral function. We also identify an “intermediate regime” where none of the established pictures applies, and the generally perceived hopping regime is found to be at a very limited end in the proposed regime paradigm.

Antiferromagnetic State in κ-type Molecular Conductors: Spin Splitting and Mott Gap

We numerically investigate the dynamical properties of $\kappa$-type molecular conductors in their antiferromagnetic Mott insulating state. By treating the extended Hubbard model on the two-dimensional $\kappa$-type lattice within the Lanzcos exact diagonalization method, we calculate the one-particle spectral function $A(\boldsymbol{k}, \omega)$ and the optical absorption spectra taking advantage of twisted boundary conditions. We find spin splitting in $A(\boldsymbol{k}, \omega)$ predicted by a previous Hartree-Fock study [M. Naka et al., Nat. Commun. 10, 4305 (2019)]; namely, their up- and down-spin components become different in the general $\boldsymbol{k}$-points of the Brillouin zone, even without the spin-orbit coupling. Furthermore, we demonstrate the variation in the optical properties near the Mott gap by the presence or absence of the antiferromagnetic order, tuned by a small staggered magnetic field.

One-particle spectral functions of the one-dimensional Fermionic Hubbard model with one fermion per site at zero and finite magnetic fields

Here the line shape of the up- and down-spin one-particle spectral functions at and in the (k,energy)-plane's vicinity of their cusp singularities is studied for the Mott-Hubbard insulator described by the 1D Hubbard model with one fermion per site at zero and finite magnetic fields. At zero field they can be accessed in terms of electrons by photoemission experiments. At finite field, such functions and corresponding interplay of correlations and magnetic-field effects refer to an involved non-perturbative many-particle problem that is poorly understood. The Mott-Hubbard gap that separates the addition and removal spectral functions is calculated for all spin densities and interaction values. The qualitative differences in the one-particle properties of the Mott-Hubbard insulator and corresponding doped insulator are also investigated. The relation of our theoretical results and predictions to both condensed-matter and ultracold spin-1/2 atom systems is discussed.

How to read between the lines of electronic spectra: the diagnostics of fluctuations in strongly correlated electron systems

While calculations and measurements of single-particle spectral properties often offer the most direct route to study correlated electron systems, the underlying physics may remain quite elusive, if information at higher particle levels is not explicitly included. Here, we present a comprehensive overview of the different approaches which have been recently developed and applied to identify the dominant two-particle scattering processes controlling the shape of the one-particle spectral functions and, in some cases, of the physical response of the system. In particular, we will discuss the underlying general idea, the common threads and the specific peculiarities of all the proposed approaches. While all of them rely on a selective analysis of the Schwinger–Dyson (or the Bethe–Salpeter) equation, the methodological differences originate from the specific two-particle vertex functions to be computed and decomposed. Finally, we illustrate the potential strength of these methodologies by means of their applications the two-dimensional Hubbard model, and we provide an outlook over the future perspective and developments of this route for understanding the physics of correlated electrons.

Functional Renormalization Group Analysis on the Spectral Function in One-Dimensional Excitonic Insulators

We analyze the one-particle spectral function for the model of Ta2NiSe5 by utilizing the functional renormalization group (fRG) method. By properly accounting for one-dimensional fluctuation effect...

Effects of finite-range interactions on the one-electron spectral properties of one-dimensional metals: Application to Bi/InSb(001)

We study the one-electron spectral properties of one-dimensional interacting electron systems in which the interactions have finite range. We employ a mobile quantum impurity scheme that describes the interactions of the fractionalized excitations at energies above the standard Tomonga-Luttinger liquid limit and show that the phase shifts induced by the impurity describe universal properties of the one-particle spectral function. We find the explicit forms in terms of these phase shifts for the momentum dependent exponents that control the behavior of the spectral function near and at the (k,omega)-plane singularities where most of the spectral weight is located. The universality arises because the line shape near the singularities is independent of the short-distance part of the interaction potentials. For the class of potentials considered here, the charge fractionalized particles have screened Coulomb interactions that decay with a power-law exponent l>5. We apply the theory to the angle-resolved photo-electron spectroscopy (ARPES) in the highly one-dimensional bismuth-induced anisotropic structure on indium antimonide Bi/InSb(001). Our theoretical predictions agree quantitatively with both (i) the experimental value found in Bi/InSb(001) for the exponent alpha that controls the suppression of the density of states at very small excitation energy omega and (ii) the location in the (k,omega) plane of the experimentally observed high-energy peaks in the ARPES momentum and energy distributions. We conclude with a discussion of experimental properties beyond the range of our present theoretical framework and further open questions regarding the one-electron spectral properties of Bi/InSb(001).

One-particle spectral function singularities in a one-dimensional gas of spin-1/2 fermions with repulsive delta-function interaction

The momentum, fermionic density, spin density, and interaction dependencies of the exponents that control the (k,ω)-plane singular features of the one-fermion spectral functions of a one-dimensional gas of spin-1/2 fermions with repulsive delta-function interaction both at zero and finite magnetic field are studied in detail. Our results refer to energy scales beyond the reach of the low-energy Tomonaga-Luttinger liquid and rely on the pseudofermion dynamical theory for integrable models. The one-fermion spectral weight distributions associated with the spectral functions studied in this paper may be observed in systems of spin-1/2 ultra-cold fermionic atoms in optical lattices.

Many-body approach to Luttinger's theorem for the Kondo lattice

A numerical verification of Luttinger's theorem, based on a recently developed many-body approach, is given for the Kondo-lattice model. For a two-dimensional lattice the completely localized spins $(S=1/2)$ are found to contribute to the Fermi sea volume as if they were electrons, which is in agreement with Oshikawa's topological proof of Luttinger's theorem. Underpinning this result we explicitly calculate the momentum-resolved one-particle spectral function showing nearly dispersionless excitations clearly below the Fermi level for different values of the conduction electron filling. Numerical integration over momentum and energy always leads to the correct particle number of the localized spins according to the well-accepted picture of a large Fermi surface. In this paper, a first many-body approach is shown, which is able to reproduce the correct value of Luttinger's theorem for this model.

Spectra of correlated many-electron systems: From a one- to a two-particle description

State-of-the-art spectroscopic techniques allow for a comprehensive understanding of one-electron excitations in various physically interesting and/or technologically relevant materials. While for weakly-correlated systems the corresponding one-particle spectral function A(ω, k) contains essentially all information about their physical properties the situation is much more complicated in the presence of strong electronic correlations. In fact, in the latter case different theoretical treatments often lead to very different explanations of the origin of specific features in the spectrum. A typical example is the pseudogap in the cuprates, i.e., the momentum-selective suppression of spectral weight at the Fermi level, which has been related to spin, charge or (d-wave) pairing fluctuations by different authors. This ambiguity about the underlying physical mechanism at work can be overcome by considering two-particle correlation functions as they are able to describe the collective modes of the system and can be also related to certain ground state properties. In this work, we will present different theoretical approaches for analyzing the spectrum of correlated systems by exploiting the information contained in these two-particle correlation functions. For the specific case of the pseudogap these procedures have allowed us (1) to identify antiferromagnetic spin fluctuations as microscopic origin of this spectral feature which (2) can be related to the formation of a resonating valence bond ground state in the system.

Phenomenological three-orbital spin-fermion model for cuprates

A spin-fermion model that captures the charge-transfer properties of Cu-based high critical temperature superconductors is introduced and studied via Monte Carlo simulations. The strong Coulomb repulsion among $d$-electrons in the Cu orbitals is phenomenologically replaced by an exchange coupling between the spins of the itinerant electrons and localized spins at the Cu sites, formally similar to double-exchange models for manganites. This interaction induces a charge-transfer insulator gap in the undoped case (five electrons per unit cell). Adding a small antiferromagnetic Heisenberg coupling between localized spins reinforces the global tendency towards antiferromagnetic order. To perform numerical calculations the localized spins are considered classical, as in previous related efforts. In this first study, undoped and doped $8\times 8$ clusters are analyzed in a wide range of temperatures. The numerical results reproduce experimental features in the one-particle spectral function and the density-of-states such as $(i)$ the formation of a Zhang-Rice-like band with a dispersion of order $\sim 0.5$ eV and with rotational symmetry about wavevector $(\pi/2,\pi/2)$ at the top of the band, and $(ii)$ the opening of a pseudogap at the chemical potential upon doping. We also observed incipient tendencies towards spin incommensurability. This simple model offers a formalism intermediate between standard mean-field approximations, that fail at finite temperatures in regimes with short-range order, and sophisticated many-body techniques such as Quantum Monte Carlo, that suffer sign problems.

Spectral function of the three-dimensional system of massless Dirac electrons

We determine the one-particle spectral function for the three-dimensional system of massless Dirac electrons with the long-range Coulomb interaction. The electron self-energy is calculated within the G0W0 approximation. We find that the spectral function has a low-energy quasi-particle and a characteristic structure due to the optic plasmon mode. The present approach is appropriate for the wide range of energy scales given by Fermi energy and plasmon energy. The obtained spectral properties are brought into correspondence with the spectra of the three-dimensional topological Dirac semimetals obtained from recent angle-resolved photoemission spectroscopy (ARPES) measurements.

Dynamic Structure Factor of Ultracold Bosons in Optical Lattice

Ultracold atoms in optical lattices have been intensively investigated in recent years as they provide a very well controllable environment for observation of many-body quantum phenomena, closely mimicking physics of strongly interacting electronic systems. Here, we use the quantum rotor approach supplemented by the Bogolyubov method to investigate oneand two-particle excitations, which are a measure of inter-particle correlations. We calculate one-particle spectral function and dynamic structure factor, which can be observed using spectroscopy of cold atomic systems. Our calculations require a significant numerical effort to determine multidimensional convolutions of momentum and frequency dependent constituents functions, which we achieve using parallelised fast Fourier transform. We observe the appearance of sharp coherence peaks in the superfluid phase of the cold bosons, which closely resembles the formation of sharply defined quasiparticle excitations below Tc in cuprates or smeared excitation spectra characteristic for strongly interacting systems.

Electronic and magnetic properties of single Fe atoms on a CuN surface: Effects of electron correlations

The electronic structure and magnetic properties of a single Fe adatom on a CuN surface have been studied using density functional theory in the local spin density approximation (LSDA), the LSDA+U approach, and the local density approximation plus dynamical mean-field theory (LDA+DMFT). The impurity problem in LDA+DMFT is solved through exact diagonalization and in the Hubbard-I approximation. The comparison of the one-particle spectral functions obtained from LSDA, LSDA+U, and LDA+DMFT show the importance of dynamical correlations for the electronic structure of this system. Most importantly, we focused on the magnetic anisotropy and found that neither LSDA nor LSDA+U can explain the measured high values of the axial and transverse anisotropy parameters. Instead, the spin excitation energies obtained from our LDA+DMFT approach with exact diagonalization agree significantly better with experimental data. This affirms the importance of treating fluctuating magnetic moments through a realistic many-body treatment when describing this class of nanomagnetic systems. Moreover, it facilitates insight to the role of the hybridization with surrounding orbitals.

Dynamical Mean-Field Theory Plus Numerical Renormalization-Group Study of Spin-Orbital Separation in a Three-Band Hund Metal.

We show that the numerical renormalization group is a viable multi-band impurity solver for dynamical mean-field theory (DMFT), offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund metal problem for a three-band model on a Bethe lattice at 1/3 filling. The ground state is a Fermi liquid. The one-particle spectral function undergoes a coherence-incoherence crossover with increasing temperature, with spectral weight being transferred from low to high energies. Further, it exhibits a strong particle-hole asymmetry. In the incoherent regime, the self-energy displays approximate power-law behavior for positive frequencies only. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales.