Disentangling topological degeneracy in the entanglement spectrum of one-dimensional symmetry-protected topological phases

Article

关键词: QUANTUM SPIN CHAINS;    ANTIFERROMAGNETS;    BREAKING;    MODELS;   

DOI  :  10.1103/PhysRevB.89.125112

来源: SCIE

【 摘 要 】

One-dimensional valence bond solid (VBS) states represent the simplest symmetry-protected topological phases. We show that their ground state entanglement spectrum contains both topological and nontopological structures. For the SO(3) symmetric VBS states with odd-integer spins, the twofold topological degeneracy is associated with an underlying Z(2) x Z(2) symmetry that protects the corresponding topological phase. In general, for the SO(2S + 1) symmetric VBS states with integer spins S, the corresponding protecting symmetry is identified as the (Z(2) x Z(2))(S) symmetry, yielding the 2(S)-fold topological degeneracy. The topological degeneracy and associated protecting symmetry can be identified by a nonlocal unitary transformation, which changes the topological order of the VBS states into conventional ferromagnetic order.

【 授权许可】

Free