Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order

@article{Chen2010LocalUT,
  title={Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order},
  author={Xie Chen and Zheng-Cheng Gu and Xiao-Gang Wen},
  journal={Physical Review B},
  year={2010},
  volume={82},
  pages={155138}
}
Two gapped quantum ground states in the same phase are connected by an adiabatic evolution which gives rise to a local unitary transformation that maps between the states. On the other hand, gapped ground states remain within the same phase under local unitary transformations. Therefore, local unitary transformations define an equivalence relation and the equivalence classes are the universality classes that define the different phases for gapped quantum systems. Since local unitary… 
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