I've been reading about the Monte Carlo sign problem, and I am a little confused about its current status. Specifically, after reading this post
I am confused on whether or not we can simulate "fermi hamiltonians away from special symmetry points". For example, in this article, the sign problem is solved for "a class of lattice field theories involving massless fermions". However, in this paper by Ceperley and Wagner, they discuss a first principles Monte Carlo to correlated electron systems, and make no discussion of the former solution. In this paper by Ferris, an unbiased Monte Carlo is introduced that "has been shown to mitigate the sign problem given a sufficiently large bond dimension". Finally, there is also Majorana Monte Carlo, which uses the Majorana representation to simulate "a class of spinless fermion models on bipartite lattices at half filling and with arbitrary range of (unfrustrated) interactions".
So my question is this: the sign problem in Monte Carlo seems to be partially solved at this point. Not only can we simulate simple fermionic systems, but recent progress in the field has led us to understand more complex and varied models. Therefore, at this point in time, what are the limitations of Monte Carlo in simulating fermionic systems? That is, what can tensor network techniques like DMRG and PEPS do that QMC can't?