Abstract: The fermion sign problem tends to stymie exploration of
highly entangled phases of fermions, such as those relevant for heavy
fermion quantum criticality. In this talk, I will present recent
progress in simulating Fermi and non-Fermi liquids in the context of
Kondo lattice systems. One of the new ideas is to consider systems
with a dimensional mismatch between the conduction electrons and the
local moments, which allows for sign-problem-free simulations even in
the presence of repulsive electronic interactions while maintaining a
Fermi surface. Time permitting, I will also discuss some results for
coupled multi-channel Kondo impurities that can lead to non-Fermi
liquid physics. Refs: arXiv: 2204.00029, 2005.10278.