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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

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Effective Theory for Strongly Attractive One-Dimensional Fermions.

Timothy G Backert¹, Fabian Brauneis¹, Matija Čufar^2,3

¹Technische Universität Darmstadt, Department of Physics, 64289 Darmstadt, Germany.

Physical Review Letters

|August 12, 2025

Summary

We simplify studies of strongly interacting two-component fermions by mapping them to a weakly interacting system. This approach uses effective interactions between fermions and bosonic dimers, enabling perturbation theory for complex systems.

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Area of Science:

Quantum physics
Condensed matter physics
Atomic physics

Background:

Studying strongly interacting many-body systems is computationally challenging.
Two-component Fermi systems exhibit complex behavior under attractive interactions.

Purpose of the Study:

To develop a simplified theoretical framework for strongly interacting two-component Fermi systems.
To enable the application of perturbation theory to previously intractable problems.

Main Methods:

Analytical solution of the few-body scattering problem using Bethe ansatz.
Engineering effective interactions between fermions and bosonic dimers.
Mapping the strongly interacting system to a weakly interacting effective model.

Main Results:

The few-body scattering problem is analytically solvable.
Effective interactions between fermions and dimers are derived.
The system can be mapped to a weakly interacting model, allowing perturbation theory.

Conclusions:

Strongly interacting two-component Fermi systems can be effectively treated as weakly interacting systems.
This simplification opens new avenues for studying complex Fermi gases, including impurity problems.