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Journal de Physique IV (Proceedings)

New method for evaluation of finite-energy few-electron spectral function expressions

J. M. P. Carmelo, Karlo Penc, Pedro D Sacramento, R. Claessen

Published Apr 1, 2004• 0 citations
Publisher

Abstract

We present a method for the calculation of few-electron spectral functions of the one-dimensional Hubbard model which relies on a pseudofermion description introduced recently in Ref. [6]. The spectral functions are expressed as a convolution of pseudofermion dynamical correlation functions. Our general method involves the direct evaluation of the matrix elements of pseudofermion operators between the ground state and the excited states. We briefly discuss the application of our general method to the study of the unusual finite-energy spectral properties observed in the quasi-one-dimensional organic conductor TTF-TCNQ.

DOI
10.1051/jp4:2004114008

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We present a method for the calculation of few-electron spectral functions of the one-dimensional Hubbard model which relies on a pseudofermion description introduced recently in Ref. [6]. The spectral functions are expressed as a convolution of pseudofermion dynamical correlation functions. Our general method involves the direct evaluation of the matrix elements of pseudofermion operators between the ground state and the excited states. We briefly discuss the application of our general method to the study of the unusual finite-energy spectral properties observed in the quasi-one-dimensional organic conductor TTF-TCNQ.
We extend to initial ground states with zero spin density m = 0 the expressions provided by the pseudofermion dynamical theory (PDT) for the finite-energy one- and two-electron spectral-weight distributions of a one-dimensional (1D) correlated metal with on-site particle-particle repulsion. The spectral-function expressions derived in this paper were used in recent successful and detailed theoretical studies of the finite-energy singular features in photoemission of the organic compound tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) metallic phase. Our studies take into account spectral contributions from types of microscopic processes that do not occur for finite values of the spin density. Expressions for the spectral functions in the vicinity of the singular border lines which also appear in the TTF- TCNQ spectral-weight distribution are derived. In addition, the PDT expressions are generalized for electronic densities in the vicinity of half filling. Further details on the processes involved in the applications to TTF-TCNQ are reported. Our results are useful for the further understanding of the unusual spectral properties observed in low-dimensional organic metals and also provide expressions for the one- and two-atom spectral functions of a correlated quantum system of ultracold fermionic atoms in a 1D optical lattice with on-site two-atom repulsion.
This thesis report deals with the 1D Hubbard model and the quantum objects that diagonalize the normal ordered Hubbard hamiltonian, among those the so called PseudoFermions (PFs). These PFs have no residual energy interactions, are eta-spin and spin zero objects, and are the scatterers and the scattering centers of the theory. The S-matrix of this representation is a simple phase factor, involving the phase shifts of the zero energy forward momentum scattering events. A PF dynamical theory is developed and applied to the one-electron removal and lower Hubbard band addition cases. For any value of the on-site effective Coloumb repulsion and electronic density, and in the limit of zero magnetization, we derive closed form expressions for these spectral functions, showing the emergence of the power-law type behavior of correlation functions of Luttinger liquids. However, our expressions are valid for the entire elementary excitation energy bandwidth. The singular behavior of the theoretical spectral weight leads to a spectral weight distribution detectable by photo emission and photo absorption experiments. As an important contribution to the understanding of quasi 1D materials, we are able to reproduce for the whole energy bandwidth, the experimental spectral distributions recently found for the organic compound TTF-TCNQ. This confirms the validity of the PF dynamical theory, and provides a deeper understanding of low dimensional correlated systems.
The momentum and energy dependence of the weight distribution in the vicinity of the one-electron spectral-function singular branch lines of the 1D Hubbard model is studied for all values of the electronic density and on-site repulsion U . To achieve this goal, we use the recently introduced pseudofermion dynamical theory. Our predictions agree quantitatively for the whole momentum and energy bandwidth with the peak dispersions observed by angle-resolved photoelectron spectroscopy in the quasi-1D organic conductor TTF-TCNQ.
Abstract. In this paper we derive general expressions for few-electron spectral functions of the one-dimensional Hubbard model for values of the excitation energy in the vicinity of the M th upper-Hubbard band lower limit. Here M = 1, 2,... is the rotated-electron double occupation, which vanishes for the ground state and is a good quantum number for all values of the on-site Coulomb repulsion U. Our studies rely on a combination of symmetries of the model with a recent finite-energy holon and spinon description of the quantum problem. We apply our general scheme to the one-electron addition spectral function, dynamical structure factor, and spin singlet Cooper pair addition spectral function. Our results provide physically interesting information about the finite-energy spectral properties of the many-electron one-dimensional quantum liquid. PACS numbers: 71.10.Fd, 64.60.Fr, 11.30.-j, 71.10.PmOne and Two-Electron Spectral Function Expressions... 2 1.
The momentum, electronic density, spin density, and interaction dependences of the exponents that control the ( k , ω ) -plane singular features of the σ = ↑ , ↓ one-electron spectral functions of the 1D Hubbard model at finite magnetic field are studied. The usual half-filling concepts of one-electron lower Hubbard band and upper Hubbard band are defined in terms of the rotated electrons associated with the model Bethe-ansatz solution for all electronic density and spin density values and the whole finite repulsion range. Such rotated electrons are the link of the non-perturbative relation between the electrons and the pseudofermions. Our results further clarify the microscopic processes through which the pseudofermion dynamical theory accounts for the one-electron matrix elements between the ground state and excited energy eigenstates.