Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2008-05-15
Condens. Matter Phys. 11, 425 (2008)
Physics
Condensed Matter
Strongly Correlated Electrons
18 pages, 8 figures
Scientific paper
We derive an alternative representation for the $f$-electron spectral function of the Falicov-Kimball 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 Wiener-Hopf sum equation approach and Szeg\"o's theorem, we can derive exact analytic formulas for the large-time 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.
Freericks James K.
Shvaika A. M.
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