  To reduce the rapidly growing computational cost of the dual fermion lattice
calculation with increasing system size, we introduce two embedding schemes.
One is the real fermion embedding, and the other is the dual fermion embedding.
Our numerical tests show that the real fermion and dual fermion embedding
approaches converge to essentially the same result. The application on the
Anderson disorder and Hubbard models shows that these embedding algorithms
converge more quickly with system size as compared to the conventional dual
fermion method, for the calculation of both single-particle and two-particle
quantities.
