The fermion sign problem often stymies exploration of strongly correlated quantum systems. Recently, new ideas have emerged on how to construct "designer Hamiltonians" which do not suffer from the sign problem, while still hosting highly entangled phases of matter. In this talk, I will present results on two new directions: (a) A model of competing antiferromagnetism and nodal d-wave superconductivity. (b) Models of non-Fermi liquids in Kondo lattice systems. In both cases, the phase diagram hosts interesting critical phenomena as well, and I will also discuss field-theoretic approaches to understand the corresponding universal quantities.
References: arXiv 1807.08202, 2005.10278 and 2009.06644