  We investigate a four-impurity Anderson model where localized orbitals are
located at vertices of a regular tetrahedron and find a novel fixed point in
addition to the ordinary Fermi liquid phase. That is characterized by
unscreened scalar chirality of a tetrahedron. In this phase, parafermions
emerges in the excitation spectrum and quasiparticle mass diverges as 1/|T
log^3 T| at low temperatures (T). The diverging effective mass is a
manifestation of singular Fermi liquid states as in the underscreened Kondo
problem. Between the two phases, our Monte Carlo results show the existence of
a non Fermi liquid critical point where the Kondo effects and the intersite
antiferromagnetic interactions are valanced. Singular behaviors are prominent
in the dynamics and we find that the frequency (omega) dependence of the
self-energy (Sigma) is the marginal Fermi liquid like, -Im Sigma \sim |omega|.
