  We present a new approach to some four-fermion lattice field theories which
we call the generalized fermion bag approach. The basic idea is to identify
unpaired fermionic degrees of freedom that cause sign problems and collect them
in a bag. Paired fermions usually act like bosons and do not lead to sign
problems. A resummation of all unpaired fermion degrees of freedom inside the
bag is sufficient to solve the fermion sign problem in a variety of interesting
cases. Using a concept of duality we then argue that the size of the fermion
bags is small both at strong and weak couplings. This allows us to construct
efficient algorithms in both these limits. Using the fermion bag approach, we
study the quantum phase transition of the 3D massless lattice Thirrring model
which is of interest in the context of Graphene. Using our method we are able
to solve the model on lattices as large as $40^3$ with moderate computational
resources. We obtain the precise location of the quantum critical point and the
values of the critical exponents through this study.
