Monday, May 16, 2016

condensed matter - Definition of short range entanglement


When studying Symmetry Protected Topological phases, one needs to define what a short range entangled (SRE) states means. But there appears to be different definitions that are not equivalent to each other. In http://arxiv.org/abs/1106.4772, Xiao-Gang Wen defined SRE states to be a state that can be transformed into the unentangled state (direct-product state) through a local unitary evolution. This implies in particular, that there cannot be SPT phases with trivial symmetry, because states with trivial symmetry can always be unitarily evolved to a product state. This is apparently contradicted to Kitaev's notation of SRE. In http://arxiv.org/abs/1008.4138, Kitaev said that there can be non-trivial SPT phases for a Majorana chain with trivial symmetry in 1+1d characterized by dangling Majorana modes at the two ends. My question is, what is Kitaev's definition of SRE (I cannot find a reference where Kitaev explicitly defined this), and how is it differed from Wen's definition. Apparently, If a state is SRE in Wen's definition, then it is SRE in Kitaev's definition.




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