A systematic method for Schrieffer-Wolff transformation and its generalizations

TL;DR

This paper introduces a rigorous, systematic method for calculating the generator of the Schrieffer-Wolff transformation, enhancing its applicability across various quantum many-body models.

Contribution

A new, systematic approach for deriving the generator of the Schrieffer-Wolff transformation, demonstrated on models from multiple quantum physics fields.

Findings

Method successfully applied to models in electron systems, quantum optics, and cavity QED.

Provides a more rigorous alternative to heuristic calculation methods.

Applicable to a broad class of quantum many-body Hamiltonians.

Abstract

Schrieffer-Wolff transformation is extensively used in quantum many-body physics to calculate the low energy effective Hamiltonian. It offers a perturbative method to understand the renormalization effects in the strong coupling regime of the quantum many-body models. The generator for Schrieffer-Wolff transformation is calculated using heuristic methods. It is highly desirable to have a rigorous, systematic and simple method for the calculation of generator for this highly important transformation. In this paper, we put forward such a method. We demonstrate our method by applying it to few well-known models from various fields like strongly correlated electron systems, quantum optics and cavity quantum electrodynamics. Our method can be applied to a broad class of quantum many-body Hamiltonians.