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Physical review B
We investigate the phase diagram of a quantum spin-1 chain whose Hamiltonian is invariant under a global onsite A_4, translation and lattice inversion symmetries. We detect different gapped phases characterized by SPT order and symmetry breaking using matrix product state order parameters. We observe a rich variety of phases of matter characterized by a combination of symmetry breaking and symmetry fractionalization and also the interplay between the onsite and spatial symmetries. Examples ofdoi:10.1103/physrevb.94.045136 fatcat:r4gylhsdg5auveec3olmjzf7u4