Berlin 2024 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 7: Poster (joint session MP/QI)

MP 7.11: Poster

Dienstag, 19. März 2024, 11:00–13:00, Poster B

Perturbative Series Expansions for Two-Particle Bound-State Energies in the Thermodynamic Limit: A Green's Function Approach — •Maximilian Bayer, Patrick Adelhardt, and Kai Phillip Schmidt — Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstr. 7, 91058 Erlangen, Germany

The investigation of (quasi-)particle bound states has been a focal point in quantum mechanics research, tracing its roots back to the solutions of the Hydrogen atom. In the realm of solid-state systems, the emergence of two-quasi-particle bound-states, such as excitons, Cooper pairs or magnon-magnon bound-states in spin systems, gives rise to unique material properties. Our interest lies in developing general techniques for systematically computing the energies associated with such bound-states on lattice systems in a perturbative manner.

We introduce an approach based on zero-temperature Green's functions (Resolvents), capable of generating series expansions for these energies in the thermodynamic limit, eliminating the need for exact diagonalization and Rayleigh-Schrödinger perturbation theory on finite systems. This technique is universal in the dimensionality of the system and accommodates fermionic, bosonic, and hard-core bosonic particles, only requiring finite-range interactions.

By reducing the eigenvalue equation into the determinant of a finite matrix we obtain a finite expression even for infinite systems. This expression allows for the extraction of bound-state energies either exactly for fixed perturbation parameters or in the form of a power series, if such a series exists.

Keywords: Bound-states; Perturbation Theory; Green's function; spin systems