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1. how to construct the reduced density matrix from single particle wf?
2. if not possible, how to evaluate the covariance matrix, i.e, <>?
3. why don't we just solve E_i, and xi_i, then S_A, but in this way, it seems no info of subregion B is involved here.
4. d-wave superconductor in real space,
5. S_A, in Borchmann, why not good?
1. If there is other internal degree of freedom in the system, for example, spin dof. For the covariance matrix, do we trace the internal dof out or write it like [<c_{i}^dagger>]