Further investigate the effect of the modified projection manifold

[bsonghao]

• [x] Only introduce T1 and uses its initial constant value along the propagation

[bsonghao]

• [ ] Calculate quasi-particle density from the Feymann-Hellmann theorem: Take partial derivatives over the matrix elements of the Bogoliubov transformed Hamiltonian.

[bsonghao]

• [x] Calculate constant Z residual without introducing the modified projection manifold

[bsonghao]

• [x] Calculate constant Z residual without introducing the modified projection manifold

603be91a317b71502e8563565aa75c4bda7ffdc1 implement the idea but get worse results