Solving real time evolution problems by constructing excitation operators

TL;DR

This paper introduces a method for solving the time evolution of observables in interacting fermion systems by constructing excitation operators, enabling analysis beyond traditional perturbation techniques.

Contribution

The paper presents a novel approach to compute real-time dynamics in interacting fermion systems using excitation operators, which simplifies the problem to matrix diagonalization.

Findings

Successfully applied to a toy model inspired by the Hubbard model

Calculated nonequilibrium current in the single impurity Anderson model

Demonstrated the method's advantage over perturbation theory

Abstract

In this paper we study the time evolution of an observable in the interacting fermion systems driven out of equilibrium. We present a method for solving the Heisenberg equations of motion by constructing excitation operators which are defined as the operators A satisfying [H,A]=\lambda A. It is demonstrated how an excitation operator and its excitation energy \lambda can be calculated. By an appropriate supposition of the form of A we turn the problem into the one of diagonalizing a series of matrices whose dimension depends linearly on the size of the system. We perform this method to calculate the evolution of the creation operator in a toy model Hamiltonian which is inspired by the Hubbard model and the nonequilibrium current through the single impurity Anderson model. This method is beyond the traditional perturbation theory in Keldysh-Green's function formalism, because the excitation energy \lambda is modified by the interaction and it will appear in the exponent in the function of time.