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AIP conference proceedings

Spectral densities of one-dimensional Pauli conductor obtained via exact diagonalization technique

O. O. Vorobyov, R. Ya. Stetsiv, Yurij V. Holovatch, Bertrand Berche, N. N. Bogolyubov, R. Folk

Published Jan 1, 2009• 2 citations
Publisher

Abstract

We investigate the energy spectrum of one‐dimensional ionic conductor described with Pauli statistics taking into account ion transfer as well as the short‐range non‐local correlation between particles. Both commutator and anticommutator Green’s functions constructed of Pauli creation and annihilation operators are calculated using exact diagonalization technique on the basis of finite ionic chains with periodic boundary conditions. The frequency dependencies of one‐particle spectral densities are calculated. In the limit of vanishing correlation strength the results are compared with the ones obtained by means of fermionization procedure while for different correlation strengths the results are compared to the ones obtained via exact diagonalization technique for similar systems described with Fermi statistics.

DOI
10.1063/1.3284416

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We investigate the energy spectrum of one‐dimensional ionic conductor described with Pauli statistics taking into account ion transfer as well as the short‐range non‐local correlation between particles. Both commutator and anticommutator Green’s functions constructed of Pauli creation and annihilation operators are calculated using exact diagonalization technique on the basis of finite ionic chains with periodic boundary conditions. The frequency dependencies of one‐particle spectral densities are calculated. In the limit of vanishing correlation strength the results are compared with the ones obtained by means of fermionization procedure while for different correlation strengths the results are compared to the ones obtained via exact diagonalization technique for similar systems described with Fermi statistics.
We focus on the features of spectra and diagrams of states obtained via exact diagonalization technique for finite ionic conductor chain in periodic boundary conditions.One dimensional ionic conductor is described with the lattice model where ions are treated within the framework of "mixed" Pauli statistics.The ion transfer and nearest-neighbour interaction between ions are taken into account.The spectral densities and diagrams of states for various temperatures and values of interaction are obtained.The conditions of transition from uniform (Mott insulator) to the modulated (charge density wave state) through the superfluid-like state (similar to the state with the Bose-Einstein condensation observed in hard-core boson models) are analyzed.
We determine the one-particle spectral function and the corresponding derived quantities for the conducting chain lattice with the finite inter-chain hopping t⊥t_\perpt⊥​ and the three-dimensional long-range Coulomb electron-electron interaction. The standard G0W0G_{0}W_{0}G0​W0​ approximation is used. It is shown that, due to the optical character of the anisotropic plasmon dispersion caused by the finite t⊥t_\perpt⊥​, the low energy quasi-particle δδδ-peak appears in the spectral function in addition to the hump present at the energies of the order of plasmon energy. The particular attention is devoted to the continuous cross-over from the non-Fermi liquid to the Fermi liquid regime by increasing t⊥t_\perpt⊥​. It is shown that the spectral weight of the hump transfers to the quasi-particle as the optical gap in the plasmon dispersion increases together with t⊥t_\perpt⊥​, with the quasi-particle residuum ZZZ behaving like −(ln⁡t⊥)−1- (\ln t_{\perp})^{-1}−(lnt⊥​)−1 in the limit t⊥→0t_{\perp}\to 0t⊥​→0. Our approach is appropriate for the wide range of energy scales given by the plasmon energy and the width of the conduction band, and is complementary to the Luttinger liquid techniques that are limited to the low energy regime close to the Fermi surface.
Abstract Motivated by the recent progress in time-resolved nonequilibrium spectroscopy in condensed matter, we study an optically excited one-dimensional ionic Hubbard model by exact diagonalization. The model is relevant to organic crystals, transition metal oxides, or ultracold atoms in optical lattices. We implement numerical pump-probe measurements to calculate time-dependent conductivity and single-particle spectral functions. In general, short optical excitation induces a metallic behavior imprinted as a Drude peak in conductivity or an in-gap density of states. In a Mott insulator, we find that the induced Drude peak oscillates at the pump frequency and its second harmonic. The former comes from the oscillation of currents, and the latter from the interference of single- and three-photon excited states. In a band insulator, the Drude peak oscillates only at the pump frequency, and quantities such as the double occupancy do not oscillate. The absence of the second harmonic oscillation is due to the degeneracy of multi-photon excited states. The in-gap density of states in both insulators correlates with the Drude weight and the energy absorption for weak pumping. Strong pumping leads to saturation of the in-gap density of states and to suppression of the Drude weight in the Mott regime. We have also checked that the above features are robust for insulators in the intermediate parameter range. Our study demonstrates the distinct natures of the multi-photon excited states in two different insulators.
Abstract Multiparticle thermodynamic Green’s functions, defined in terms of grand canonical ensemble averages of time-ordered products of creation and annihilation operators, are interpreted as tracing the amplitude for time-developing correlated interacting particle motions taking place in the background of a thermal ensemble. Under equilibrium conditions, time-translational invariance permits the one-particle thermal Green’s function to be represented in terms of a single frequency, leading to a Lehmann spectral representation whose frequency poles describe the energy spectrum. This Green’s function has finite values for both t>t′ and t<t′ (unlike retarded Green’s functions), and the two parts G1> and G1< (respectively) obey a simple proportionality relation that facilitates the introduction of a spectral weight function: It is also interpreted in terms of a periodicity/antiperiodicity property of a modified Green’s function in imaginary time capable of a Fourier series representation with imaginary (Matsubara) frequencies. The analytic continuation from imaginary time to real time is discussed, as are related commutator/anticommutator functions, also retarded/advanced Green’s functions, and the spectral weight sum rule is derived. Statistical thermodynamic information is shown to be embedded in physical features of the one- and two-particle thermodynamic Green’s functions.
In this work, we consider NNN-fold degenerate DDD-dimensional electron gas with spherical Fermi surface and arbitrary forward-scattering density-density interaction transferring small momentum compared to the Fermi momentum kFk_{\mathrm{F}}kF​. The dimensional reduction that is mathematically equivalent to the Haldane patch construction and similar multidimensional bosonization techniques, provides a natural map of two-point DDD-dimensional correlation functions (fermion Green function, susceptibilities etc.) onto effective one-dimensional (1D) correlators with the same diagrammatic structure, which can be evaluated exactly within a 1D bosonizable (Gaussian) theory. We then apply this formalism to evaluate the fermion Green function, pair and charge/flavor susceptibilities, as well as the composite correlation functions for the case of a finite-range interaction, where the interaction range Rs≫1/kFR_{\mathrm{s}} \gg 1/k_{\mathrm{F}}Rs​≫1/kF​ is large compared to the Fermi wavelength. First, we find that the single-particle spectral function remains Fermi-liquid-like which is fully consistent with the previous research. In contrast to the single-particle sector, the many-body channels are efficiently dressed by finite-range interactions, and this dressing is fully equivalent to the one-loop renormalization group (RG), which is also in line with previous multidimensional bosonization results. Within the forward-scattering model, stable long-range order is not possible, and relevant susceptibilities demonstrate singular power-law scaling with temperature TTT at T→0T \to 0T→0. The rest of the abstract is in the PDF.