Krylov-Bogoliubov-Mitropolsky Averaging Used to Construct Effective Hamiltonians in the Theory of Strongly Correlated Electron Systems

TL;DR

This paper introduces a general averaging method based on Krylov-Bogoliubov-Mitropolsky techniques for deriving effective Hamiltonians in strongly correlated electron systems, simplifying complex models like Hubbard to t-J and Anderson to Kondo.

Contribution

It demonstrates the application of averaging methods to construct effective Hamiltonians, offering advantages over existing approaches in correlated electron physics.

Findings

Successfully derives t-J and Kondo Hamiltonians from Hubbard and Anderson models.

Highlights the generality and advantages of the averaging method.

Provides a new tool for analyzing strongly correlated systems.

Abstract

We show that the Krylov-Bogoliubov-Mitropolsky averaging in the canonical formulation can be used as a method for constructing effective Hamiltonians in the theory of strongly correlated electron systems. As an example, we consider the transition from the Hamiltonians of the Hubbard and Anderson models to the respective Hamiltonians of the t-J and Kondo models. This is a very general method, has several advantages over other methods, and can be used to solve a wide range of problems in the physics of correlated systems.