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arXiv · 1109.1205

Krylov-space approach to the equilibrium and the nonequilibrium single-particle Green's function

Matthias Balzer·Nadine Gdaniec·Michael Potthoff
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Abstract

The zero-temperature single-particle Green's function of correlated fermion models with moderately large Hilbert-space dimensions can be calculated by means of Krylov-space techniques. The conventional Lanczos approach consists of finding the ground state in a first step, followed by an approximation for the resolvent of the Hamiltonian in a second step. We analyze the character of this approximation and discuss a numerically exact variant of the Lanczos method which is formulated in the time domain. This method is extended to get the nonequilibrium single-particle Green's function defined on the Keldysh-Matsubara contour in the complex time plane. The proposed method will be important as an exact-diagonalization solver in the context of self-consistent or variational cluster-embedding schemes. For the recently developed nonequilibrium cluster-perturbation theory, we discuss the efficient implementation and demonstrate the feasibility of the Krylov-based solver. The dissipation of a strong local magnetic excitation into a non-interacting bath is considered as an example for applications.

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Matthias Balzer, Nadine Gdaniec, Michael Potthoff. 2011-12-01. Krylov-space approach to the equilibrium and the nonequilibrium single-particle Green's function. https://doi.org/10.1088/0953-8984%2F24%2F3%2F035603

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