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?
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.