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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 stochastic and non-stochastic methods to characterize matter in extreme environments. These are realized for example in collisions between neutron stars (neutron star mergers) which are widely believed to be the sites of r-process nucleosynthesis (i.e. where the heavy elements are made!).

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. 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.