Reconstruction of Spectral Densities from Incomplete Continued Fractions

M. Drawid, J. W. Halleý

M. Drawid, J. W. Halleý

R. Hayn, P. Lombardo, Konrad Matho

We present the continued fraction method (CFM) as a microscopic approximation to the spectral density of the Hubbard model in the correlated metal phase away from half filling. The quantity expanded as a continued fraction is the single-particle Green's function. Leading spectral moments are taken into account through a set of real expansion coefficients, as known from the projection technique. Further stages are added to the continued fraction, with complex coefficients, thus defining a terminator function. This enables us to treat the entire spectral range of the Green's function on equal footing and determine the energy scale of the Fermi liquid quasiparticles by minimizing the total energy. The solution is free of phenomenological parameters and remains well defined in the strong-coupling limit, near the doping-controlled metal-insulator transition. Our results for the density of states agree reasonably with those from several variants of the dynamical mean-field theory. The CFM requires minimal numerical effort and can be generalized in several ways that are interesting for applications to real materials.

David A. Mazziotti

Alessandro Cuccoli, V. Tognetti, A. A. Maradudin +2 more

We show how the results of classical molecular-dynamics simulations can be used to improve the calculation of quantum spectral densities of anharmonic crystals. In particular we show that the spectral density C(k,\ensuremath{\omega}) of the displacement correlation function for a quantum chain of N atoms interacting through a nearest-neighbor Lennard-Jones potential, can be calculated accurately in the following way. C(k,\ensuremath{\omega}) is expressed in the form of a continued fraction, whose coefficients are given in terms of its even-frequency moments. The latter, up through the sixth, are calculated from an effective potential that includes the effects of quantum fluctuations. The continued fraction is then terminated by the use of a termination parameter that is determined from a fit of the same continued fraction to the spectral density calculated by means of a classical molecular-dynamics simulation.

Carsten Raas, Götz Silvester Uhrig