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We describe the thermodynamics of quantum matter using the non-perturbative tools of lattice field theory. Starting from particle content and interactions, we implement computational methods to characterize matter in extreme environments such as neutron star mergers and ultracold atoms.

We also explore fundamental few- and many-body problems in universal regimes in a wide range of situations across dimensions, temperatures, interaction strengths, and more. These generic quantum many-body systems present a computational challenge shared by nearly all areas of physics: from quantum chemistry to condensed matter, nuclear physics, and quantum chromodynamics. To meet that challenge, we develop new algorithms and adapt methods from other areas.