For systems of nuclei and electrons (most everything), we know the microscopic Hamiltonian extremely accurately. Paraphrasing Dirac, we know enough in principle to compute everything we'd like to know about condensed matter systems, although the equations for 10^23 particles are too difficult to solve. Therefore it is of use to develop good approximations, which are called first principles methods. In recent years, it has been demonstrated that modern first principles approaches can solve the Schroedinger equation to very high accuracy for systems ranging between 30 (accuracy of around .025 eV) and 1000 particles (accuracy of around 0.1 eV).
While first principles calculations are limited to systems too small for direct simulation of much collective pheneomena, they are now able to access systems large enough to infer low-energy physics. In this talk, I'll discuss our progress in using high-accuracy many-body simulations at the first principles level to discover and derive low-energy physics. Quantum Monte Carlo and machine learning get involved.