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arXiv:2311.02414 · Physical review. B./Physical review. B

Electronic quantum wires in extended quasiparticle picture

Klaus Morawetz, Vinod Ashokan, Kare Narain Pathak, N. D. Drummond, Gianaurelio Cuniberti

Published May 7, 2024• 0 citations
arXivHTMLPDF

Abstract

Expanding the two-particle Green's functions determines the self-energy and the polarization as well as the response function on the same footing. The correlation energy is calculated with the help of the extended quasiparticle picture, which accounts for off-shell effects. The corresponding response function leads to the same correlation energy as the self-energy in agreement with perturbation theory, provided one works in the extended quasiparticle picture. A one-dimensional quantum wire of fermions is considered and ground-state properties are calculated in the high-density regime within the extended quasiparticle picture and Born approximation. While the on-shell selfenergies are strictly zero due to Pauli-blocking of elastic scattering, the off-shell behavior shows a rich structure of a gap in the damping of excitation, which is closed when the momentum approaches the Fermi one. The consistent spectral function is presented, completing the first two energy-weighted sum rules. The excitation spectrum shows a splitting due to holons and antiholons as non-Fermi liquid behavior. A renormalization procedure is proposed by subtracting an energy constant to render the Fock exchange energy finite. The effective mass derived from meanfield approximation shows a dip analogous to the onset of Peierls instability. The reduced density matrix or momentum distribution is calculated with the help of a Pad\'e regularization repairing deficiencies of the perturbation theory. A seemingly finite step at the Fermi energy indicating Fermi-liquid behavior is repaired in this way.

DOI
10.1103/physrevb.109.205116

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Expanding the two-particle Green's functions determines the self-energy and the polarization as well as the response function on the same footing. The correlation energy is calculated with the help of the extended quasiparticle picture, which accounts for off-shell effects. The corresponding response function leads to the same correlation energy as the self-energy in agreement with perturbation theory, provided one works in the extended quasiparticle picture. A one-dimensional quantum wire of fermions is considered and ground-state properties are calculated in the high-density regime within the extended quasiparticle picture and Born approximation. While the on-shell selfenergies are strictly zero due to Pauli-blocking of elastic scattering, the off-shell behavior shows a rich structure of a gap in the damping of excitation, which is closed when the momentum approaches the Fermi one. The consistent spectral function is presented, completing the first two energy-weighted sum rules. The excitation spectrum shows a splitting due to holons and antiholons as non-Fermi liquid behavior. A renormalization procedure is proposed by subtracting an energy constant to render the Fock exchange energy finite. The effective mass derived from meanfield approximation shows a dip analogous to the onset of Peierls instability. The reduced density matrix or momentum distribution is calculated with the help of a Pad'e regularization repairing deficiencies of the perturbation theory. A seemingly finite step at the Fermi energy indicating Fermi-liquid behavior is repaired in this way.
Abstract The extended quasiparticle picture is adapted to non-Fermi systems by suggesting a Padé approximation which interpolates between the known small scattering-rate expansion and the deviation from the Fermi energy. The first two energy-weighted sum rules are shown to be fulfilled independent of the interpolating function for any selfenergy. For various models of one-dimensional Fermions scattering with impurities the quality of the Padé approximation for the spectral function is demonstrated and the reduced density matrix or momentum distribution is reproduced not possessing a jump at the Fermi energy. Though the two-fold expansion is necessary to realize the spectral function and reduced density, the extended quasiparticle approximation itself is sufficient for the description of transport properties due to cancellation of divergent terms under integration. The T-matrix approximation leads to the delay time as the time two particles spend in a correlated state. This contributes to the reduced density matrix and to an additional part in the conductivity which is presented at zero and finite temperatures. Besides a localization at certain impurity concentrations, the conductivity shows a maximum at small temperatures interpreted as onset of superconducting behaviour triggered by impurities. The Tan contact reveals the same universal behaviour as known from electron–electron scattering. Graphic abstract
Electronic states in the two-dimensional Hubbard model are studied in the doped paramagnetic states by use of the auxiliary boson approach. Four auxiliary bosons are introduced by means of the Hubbard-Stratonovich transformation within the functional integral treatment. These bosons correspond to one charge and three spin fluctuations. An effective model is formulated. Going beyond the boson fluctuations around the saddle point, the single-electron Green's function including one-loop self-energy effects of fermion-boson interaction is derived. The behavior of the fermion self-energy, spectral functions, and density of states are investigated for several values of the Coulomb interaction UUU within the limit imposed by the Stoner criterion and also for small and moderate doping concentrations $\ensuremath{\delta}$. For small doping $(\ensuremath{\delta}=0.2)$, as UUU approaches a value determined by the Stoner criterion, the spin-boson spectrum has a striking low-energy enhancement around $\mathbf{q}\ensuremath{\sim}2{\mathbf{k}}_{F}.$ This enhancement of the spin fluctuation causes a non-Fermi-liquid-like low-energy $\ensuremath{\omega}$ linear dependence in the imaginary part of the self-energy. Due to the self-energy effects, band splittings and a band narrowing are produced in the spectral functions. As a consequence of this, the density of states has pseudogap structures around the quasiparticle band with a narrow bandwidth on the Fermi energy. These features seem to be precursors of the metal-insulator (Mott-Hubbard) transition and they might be related to the spin-gap phenomena observed in high-Tc{T}_{c}Tc​ materials. Our results for the density of states, the spectral function, and the band dispersions show qualitative agreement with the data of finite-size cluster simulations.
An exactly soluble one-dimensional model of electrons interacting with order-parameter fluctuations associated with short-range order is considered. The energy and momentum dependence of the electronic self-energy and spectral function are calculated and found to exhibit non-Fermi-liquid features similar to that seen for the two-dimensional Hubbard model: a pseudogap, shadow bands, anomalies in the self-energy, and breakdown of the quasiparticle picture. Deviations from Fermi-liquid behavior are largest close to the Fermi surface and as the correlation length increases.
We study the ground-state properties of ferromagnetic quasi-one-dimensional quantum wires using the quantum Monte Carlo (QMC) method for various wire widths bbb and density parameters rs{r}_{\text{s}}rs​. The correlation energy, pair-correlation function, static structure factor, and momentum density are calculated at high density. It is observed that the peak in the static structure factor at k=2kFk=2{k}_{\text{F}}k=2kF​ grows as the wire width decreases. We obtain the Tomonaga-Luttinger liquid parameter ${K}_{\ensuremath{\rho}}$ from the momentum density. It is found that ${K}_{\ensuremath{\rho}}$ increases by about 10% between wire widths b=0.01b=0.01b=0.01 and b=0.5b=0.5b=0.5. We also obtain ground-state properties of finite-thickness wires theoretically using the first-order random phase approximation (RPA) with exchange and self-energy contributions, which is exact in the high-density limit. Analytical expressions for the static structure factor and correlation energy are derived for $b\ensuremath{\ll}{r}_{\text{s}}<1$. It is found that the correlation energy varies as b2{b}^{2}b2 for $b\ensuremath{\ll}{r}_{\text{s}}$ from its value for an infinitely thin wire. It is observed that the correlation energy depends significantly on the wire model used (harmonic versus cylindrical confinement). The first-order RPA expressions for the structure factor, pair-correlation function, and correlation energy are numerically evaluated for several values of bbb and ${r}_{\text{s}}\ensuremath{\le}1$. These are compared with the QMC results in the range of applicability of the theory.
We have carried out a comprehensive investigation of the quasiparticle properties of a two-dimensional electron gas, interacting via the long-range Coulomb interaction in the presence of bare mass anisotropy (i.e., with an elliptic noninteracting Fermi surface) by calculating the self-energy, the spectral function, the scattering rate, and the effective mass within the leading-order dynamical self-energy approximation. Our theory is exact in the high-density limit. We find anisotropic features of quasiparticle properties that are not captured by the commonly used isotropic approximation where the anisotropic effective mass is replaced by the isotropic averaged density-of-states mass. Some of these interesting results are as follows: (1) The many-body renormalization of the quasiparticle spectrum becomes highly anisotropic as the quasiparticle energy increases away from the Fermi energy; (2) the interaction-induced inelastic-scattering rate features a strong anisotropy, exhibiting an abrupt jump at different injected energies depending on the momentum direction of the injected electron; (3) the effective-mass enhancement is larger (smaller) for the light (heavy) mass, showing that the anisotropy is reduced by interactions. Our results and analysis show that the unjustified neglect of the mass anisotropy can lead to an incorrect description of quasiparticle properties of the anisotropic system and inaccurate estimates of physical quantities of interest although the use of an equivalent isotropic approximation using the density-of-states effective mass as is commonly and uncritically performed in the literature, works as a reasonable approximation in many situations. In addition to the complete random phase approximation theory for the anisotropic quasiparticles, we also provide a theory using the simpler plasmon-pole approximation, commenting on its validity for anisotropic self-energy calculations. We comment also on the interaction effect on the Fermi-surface topology, finding that the elliptic shape of the bare Fermi surface is preserved with suppressed ellipticity in the interacting system to a high degree of accuracy except in the very strongly interacting limit (and for very high bare mass anisotropy). Our theory provides a complete generalization of the existing isotropic many-body theory of interacting electrons to the corresponding anisotropic systems.
Momentum-dependent local ansatz (MLA) wavefunction approach to correlated electrons in solids has been extended to the quasiparticle excited states on the basis of the Fermi liquid picture. The quasiparticle energy is derived from the MLA-base excited state wavefunction within the single-site approximation. The quasiparticle weight and quasiparticle energy have been calculated for the Hubbard model on the hypercubic lattice in infinite dimensions as well as the simple cubic lattice. By comparing the numerical results with the single-particle excitation spectra obtained by the Green function method, it is shown that the MLA excited wavefunctions describe well the quasiparticle states in the weak and intermediate Coulomb interaction regime in the high dimensional system.