  Anomalous global symmetries, which can be realized on the boundary of
symmetry-protected topological phases, brings new phases and phase transitions
to condensed matter physics. In this work, we study a one dimensional model
with an anomalous Z2 symmetry, using the density-matrix renormalization group
method. Besides a symmetry-breaking ferromagnetic phase, we find a gapless
phase described by the SU(2)_1 conformal field theory, despite the existence of
only discrete Z_2 symmetry in the Hamiltonian. The phase transition between the
ferromagnetic phase and the gapless phase is continuous and has the same
critical scaling as in the gapless phase. Our numerical finding is compatible
of theoretical constraints on possible phases resulting from the symmetry
anomaly.
