Dark matter is a mysterious constituent of the universe, 5 times more abundant than ordinary (or visible) matter. The characterisation of its properties remains one of the most pressing problems of particle physics. In particular, dark matter could be in a degenerate quantum state in some galaxies, with novel phenomenological consequences. The proposed work would consist in studying a toy model of fermions with attractive long range interaction to mimic the peculiar properties of these galaxies, which can be done using state-of-the-art tensor network techniques. The student is expected to investigate the ground state (and thermal) properties of this quantum model, and understand which new properties may appear in the final virialized states ('halos') from quantum degeneracy pressure as compared to their classical counterpart. Because of its interdisciplinary nature, this work would be done in co-supervision with Prof. Diego Blas from Universitat Autònoma de Barcelona, and Prof. Mari Carmen Bañuls from Max Planck Institute for Quantum Optics (Garching, Germany). The student would moreover have the opportunity to visit the MPQ to work closely with Prof. Bañuls for a period of one to a few weeks (all expenses covered).