Exact closed-form unitary transformations of fermionic operators

TL;DR

This paper derives exact closed-form formulas for unitary transformations generated by single fermionic operators, enabling new analytical and numerical approaches in many-body fermionic physics.

Contribution

It provides the first closed-form expressions for such transformations, facilitating formal analysis and numerical methods in fermionic many-body systems.

Findings

Derived closed-form expressions for fermionic unitary transformations.

Demonstrated applications in block-diagonalization and Heisenberg dynamics.

Enabled new analytical and numerical techniques for fermionic systems.

Abstract

Unitary transformations play a fundamental role in many-body physics, and except for special cases, they are not expressible in closed form. We present closed-form expressions for unitary transformations generated by a single fermionic operator for Hermitian and anti-Hermitian generators. We demonstrate the usefulness of these expressions in formal analyses of unitary transformations and numerical applications involving block-diagonalization and Heisenberg dynamics. This work paves the way for new analytical treatments of unitary transformations and numerical many-body methods for fermions.