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

Area of Science:

• * Condensed Matter Physics
• * Quantum Many-Body Theory

Background:

• * Calculating the single-particle Green's function for correlated fermion models is computationally intensive.
• * Conventional Lanczos methods involve a two-step approximation for the Hamiltonian's resolvent.

Purpose of the Study:

• * To develop a numerically exact variant of the Lanczos method for calculating Green's functions.
• * To extend this method for nonequilibrium scenarios and nonperturbative responses.
• * To provide an exact-diagonalization solver for cluster-embedding schemes and nonequilibrium cluster-perturbation theory.

Main Methods:

• * Formulation of a time-domain, numerically exact Lanczos method.
• * Extension to the Keldysh-Matsubara contour for nonequilibrium Green's functions.
• * Application to self-consistent/variational cluster-embedding and nonequilibrium cluster-perturbation theory.

Main Results:

• * A variant of the Lanczos method provides a numerically exact approach.
• * The method successfully calculates nonequilibrium Green's functions for sudden Hamiltonian parameter changes.
• * Demonstrated feasibility for efficient implementation within cluster-embedding schemes.

Conclusions:

• * The proposed Krylov-space technique offers an exact-diagonalization solver for complex quantum systems.
• * This method is vital for advancing studies in nonequilibrium quantum dynamics and condensed matter physics.
• * Applicable to phenomena like magnetic excitation dissipation in quantum baths.