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

Abstract

Anomalous global symmetries, which can be realized on the boundary of symmetry-protected topological phases, bring\wlx{s} new phases and phase transitions to condensed matter physics. In this work, we study a one-dimensional model with an anomalous ${\mathbb{Z}}_2$ symmetry, using the density-matrix renormalization group method. Besides a symmetry-breaking ferromagnetic phase, we find a gapless phase described by the Tomonaga-Luttinger Liquid theory with the central charge $c=1$. Our numerical finding is compatible of theoretical constraints on possible phases resulting from the symmetry anomaly.