On the structure and convergence of the symmetric Zassenhaus formula

TL;DR

This paper introduces a symmetric Zassenhaus formula for better operator exponential disentangling, providing a recursive expansion method that enhances convergence and approximation accuracy, especially for matrices.

Contribution

It presents a novel symmetric version of the Zassenhaus formula with a recursive expansion procedure, extending convergence domain and improving approximations over the standard formula.

Findings

Recursive expansion improves convergence for matrices.

Symmetric formula yields better approximations than standard Zassenhaus.

Enlarged convergence domain demonstrated for matrix cases.

Abstract

We propose and analyze a symmetric version of the Zassenhaus formula for disentangling the exponential of two non-commuting operators. A recursive procedure for generating the expansion up to any order is presented which also allows one to get an enlarged domain of convergence when it is formulated for matrices. It is shown that the approximations obtained by truncating the infinite expansion considerably improve those arising from the standard Zassenhaus formula.