# How can we detect the topological order in 1+1D topological superconductor numerically?

I read some material in this forum and realize that entanglement entropy does not correspond to long range entanglement. Then what quantity can be used to characterize the topological order in 1+1D topological superconductor that can be obtained numerically?

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Which material? –  Qmechanic Sep 30 '13 at 18:29
For example, in discussion in the link : physics.stackexchange.com/q/37840 –  fangniuwawa Oct 1 '13 at 9:19

For simple systems, when a simple Bogoliubov-deGennes Hamiltonian is sufficient, you can calculate the band structure with periodic boundary condition. Then you calculate the band structure imposing open boundary conditions. The topological aspects usually show themselves as zero energy band crossing.

The previous method is particularly efficient when you do not need to consider the self-consistency condition for superconductivity, and/or without impurities. Adding these two effects... well I do not know other numerical method than the previous one, sorry.

I'm a bit under rush. Please ask for further precisions if you need some.

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If you bosonize the 1+1D fermion model, the fermion parity conservation becomes a $Z_2$ symmetry in the bosonize model. If the bosonize model spontaneously break such a $Z_2$ symmetry, then the 1+1D fermion model is in the topologically ordered phase. –  Xiao-Gang Wen Oct 3 '13 at 1:24