Condensed Matter Physics, 2008, vol. 11, No. 3(55), p. 425442
DOI:10.5488/CMP.11.3.425
Title:
Felectron spectral function of the FalicovKimball model and the WienerHopf sum equation approach
Author(s):

A.M. Shvaika
(Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine)
,


J.K. Freericks
(Department of Physics, Georgetown University, 37th and O Sts. NW, Washington, DC 20057, USA)

We derive an alternative representation for the felectron spectral function of the FalicovKimball model from the original one proposed by Brandt and Urbanek. In the new representation, all calculations are restricted to the real time axis, allowing us to go to arbitrarily low temperatures. The general formula for the retarded Green's function involves two determinants of continuous matrix operators that have the Toeplitz form. By employing the WienerHopf sum equation approach and Szegö's theorem, we can derive exact analytic formulas for the largetime limits of the Green's function; we illustrate this for cases when the logarithm of characteristic function (which defines the continuous Toeplitz matrix) does and does not wind around the origin. We show how accurate these asymptotic formulas are to the exact solutions found from extrapolating matrix calculations to the zero discretization size limit.
Key words:
Felectron spectral function, FalicovKimball model, WienerHopf approach, dynamical meanfield theory
PACS:
71.10.w, 71.27.+a, 71.30.+h, 02.30.Rz
