  We study the two dimensional lattice Thirring model in the presence of a
fermion chemical po- tential. Our model is asymptotically free, contains
massive fermions that mimic a baryon and light bosons that mimic pions. Hence
it is a useful toy model for QCD, especially since it too suffers from a sign
problem in the auxiliary field formulation in the presence of a fermion
chemical potential. In this work we formulate the model in both the world line
and fermion-bag representations and show that the sign problem can be
completely eliminated with open boundary conditions when the fermions are
massless. Hence we are able accurately compute a variety of interesting
quantities in the model, and these results could provide benchmarks for other
methods that are being developed to solve the sign problem in QCD.
