Erlangen 2022 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 26: Quantum Gases (Fermions)

Q 26.8: Talk

Wednesday, March 16, 2022, 12:15–12:30, Q-H10

Efficient Diagonalization Methods for Mesoscopic Fermi Systems — •Paul Hill — Physikalisches Institut, Universität Heidelberg, Deutschland

Already mesoscopic systems of interacting fermions show emergent collective phenomena such as the precursor of a quantum phase transition or cooper pairing [1,2].

These strongly correlated systems are notoriously hard to describe theoretically due to the exponential scaling of their underlying Hilbert spaces. The sparsity of typical physical Hamiltonians, however, allows us to use the Lanczos algorithm, an established numerical method in the condensed matter community. At its heart, this method seeks to identify a small sub-space of the full system on which the Hamiltonian can be efficiently diagonalized without loss of the relevant physics.

Here we use the Quanty many-body code [3] to conveniently apply the Lanczos method in the language of second quantization to the problem of few ultracold atoms interacting via s-wave scattering in a two-dimensional harmonic trap. The numerical prediction of the excitation spectrum is compared to recent experimental observations [1].

[1] Luca Bayha et al. Observing the emergence of a quantum phase transition shell by shell. Nov 2020.

[2] Marvin Holten et al. Observation of cooper pairs in a mesoscopic 2d fermi gas. Sep 2021

[3] www.quanty.org, M. W. Haverkort et al. Multiplet ligand-field theory using wannier orbitals. Apr 2012.