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Keywords:

  • Thermal Green's functions;
  • Dyson equation;
  • Hubbard model.

Abstract

We present a spectral weight conserving formalism for Fermionic thermal Green's functions that are discretized in imaginary time τ and thus periodic in imaginary (“Matsubara”) frequency i ωn. The formalism requires a generalization of the Dyson equation G (G0, Σ) and the Baym-Kadanoff-Luttinger-Ward functional for the free energy β Ω = Γ (G). A conformal transformation is used to analytically continue the periodized Matsubara Green's function to real frequencies in a way that conserves the discontinuity at t = 0 of the corresponding real-time Green's function. This allows numerical Green's function calculations of very high precision and it appears to give a well controlled convergent approximation in the τ discretization. The formalism is tested on dynamical mean field theory calculations of the paramagnetic Hubbard model.