  We present a solution to the sign problem in a class of particle-hole
symmetric Hamiltonian lattice fermion models on bipartite lattices using the
idea of fermion bags. The solution remains valid when the particle-hole
symmetry is broken through a staggered chemical potential term. This solution
allows, for the first time, simulations of some massless four-fermion models
with minimal fermion doubling and with an odd number of fermion flavors using
ultra-local actions. One can thus study a variety of quantum phase transitions
that have remained unexplored so far due to sign problems.
