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

TL;DR

This paper introduces a Krylov-space based method for calculating equilibrium and nonequilibrium single-particle Green's functions in correlated fermion models, extending existing techniques to complex time contours and demonstrating its application in cluster-perturbation theory.

Contribution

It presents a numerically exact Krylov-space approach formulated in the time domain for Green's functions, applicable to equilibrium and nonequilibrium scenarios, including complex time contours.

Findings

The method is numerically exact and efficient.

It can be applied to nonequilibrium Green's functions on the Keldysh-Matsubara contour.

Demonstrated feasibility in a magnetic excitation dissipation example.

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.