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Anomalous global symmetries, which can be realized on the boundary ofsymmetry-protected topological phases, brings new phases and phase transitionsto condensed matter physics. In this work, we study a one dimensional modelwith an anomalous Z2 symmetry, using the density-matrix renormalization groupmethod. Besides a symmetry-breaking ferromagnetic phase, we find a gaplessphase described by the SU(2)_1 conformal field theory, despite the existence ofonly discrete Z_2 symmetry in the Hamiltonian. The phase transition between theferromagnetic phase and the gapless phase is continuous and has the samecritical scaling as in the gapless phase. Our numerical finding is compatibleof theoretical constraints on possible phases resulting from the symmetryanomaly.

Phase diagram of a one-dimensional Ising model with an anomalous Z_2 symmetry