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Updated: Apr 8, 2026
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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
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On the Feasibility of Exact Unitary Transformations for Many-Body Hamiltonians
Praveen Jayakumar1,2, Tao Zeng3, Artur F Izmaylov1,2
1Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
Journal of Chemical Theory and Computation
|April 6, 2026
Summary
Exact unitary transformations in quantum systems are possible when their generator
Area of Science:
- Quantum computing
- Quantum chemistry
- Computational physics
Background:
- Exact unitary transformations are crucial for quantum many-body system analysis and simulation.
- Understanding the conditions for exact and efficient transformations is an ongoing challenge.
Purpose of the Study:
- To establish a unifying principle for exact unitary transformations.
- To identify algebraic conditions that enable efficient quantum transformations.
- To propose new methods for reducing computational costs in quantum simulations.
Main Methods:
- Analyzing the adjoint action of unitary generators within finite-dimensional operator spaces.
- Utilizing Lie algebras and their modules to derive finite Baker-Campbell-Hausdorff (BCH) expansions.
- Investigating algebraic relations between generators and transformed operators.
Main Results:
- Exact transformations occur when the adjoint action is a linear map in a finite-defined operator space, leading to a finite BCH expansion.
- Lie algebras and modules explain finite BCH expansions across known examples.
- A new class of Fermionic generators for efficient transformations is proposed.
Conclusions:
- Sufficient algebraic conditions for exact unitary transformations are established.
- New strategies for efficient quantum simulations and feasible unitary transformations are provided.
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