  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.
