  In many interesting systems, the fermion determinant becomes complex and its
phase plays a crucial role in the determination of the vacuum. For instance, in
finite density QCD at low temperature and high density, exotic fermion
condensates are conjectured to form due to such effects. When one applies the
complex Langevin method to such a complex action system naively, one cannot
obtain the correct results because of the singular-drift problem associated
with the appearance of small eigenvalues of the Dirac operator. Here we propose
to avoid this problem by adding a fermion bilinear term to the action and
extrapolating its coefficient to zero. We test this idea in an SO(4)-invariant
matrix model with a Gaussian action and a complex fermion determinant, whose
phase is expected to induce the spontaneous breaking of the SO(4) symmetry. Our
results agree well with the previous results obtained by the Gaussian expansion
method.
