  We investigate the sign problem of the fermion determinant at finite baryon
density in (1+1) dimensions, in which the ground state in the chiral limit
should be free from the sign problem by forming a chiral spiral. To confirm it,
we evaluate the fermion determinant in the continuum theory at the one-loop
level and find that the determinant becomes real as expected. The conventional
lattice formulation to implement a chemical potential is, however, not
compatible with the spiral transformation. We discuss an alternative of the
finite-density formulation and numerically verify the chiral spiral on the
finite-density lattice.
