Dedicated to Ulrich Eckern on the occasion of his 60th birthday.
Discretized thermal Green's functions†
Article first published online: 24 FEB 2012
Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Annalen der Physik
Special Issue: Quantum Dynamics of Nano-Structured Systems
Volume 524, Issue 3-4, pages 147–152, April 2012
How to Cite
Granath, M., Sabashvili, A., Strand, H.U.R. and Östlund, S. (2012), Discretized thermal Green's functions. Ann. Phys., 524: 147–152. doi: 10.1002/andp.201100262
- Issue published online: 21 MAR 2012
- Article first published online: 24 FEB 2012
- Manuscript Accepted: 19 DEC 2011
- Manuscript Received: 12 OCT 2011
- Thermal Green's functions;
- Dyson equation;
- Hubbard model.
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.