title: Krylov-space approach to the equilibrium and nonequilibrium single-particle Green's function.
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 obtain the nonequilibrium single-particle Green's function defined on the Keldysh-Matsubara contour in the complex time plane which describes the system's nonperturbative response to a sudden parameter switch in the Hamiltonian. 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 its 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.
authors.affiliation: I Institut für Theoretische Physik, Universität Hamburg, Hamburg, Germany.
authors.forename: Matthias
authors.initials: M
authors.lastname: Balzer
authors.forename: Nadine
authors.initials: N
authors.lastname: Gdaniec
authors.forename: Michael
authors.initials: M
authors.lastname: Potthoff