Exact closed-form unitary transformations of fermionic operators

• URL: http://arxiv.org/abs/2408.09636v1
• Date: Mon, 19 Aug 2024 01:43:22 GMT
• Title: Exact closed-form unitary transformations of fermionic operators
• Authors: Francesco A. Evangelista, Ilias Magoulas,
• Abstract summary: 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. This work paves the way for new analytical treatments of unitary transformations and numerical many-body methods for fermions.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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