It is rather troublesome, if at all possible, to construct the decomposition D for an arbitrary n-particle state, since this would mean one has to compute the Schmidt decomposition at each bond, to arrange the Schmidt eigenvalues in decreasing order and to choose the first χ χ c and the appropriate Schmidt eigenvectors. Mind this would imply diagonalizing somewhat generous reduced density matrices, which, depending on the system one has to simulate, might be a task beyond our reach and patience. Instead, one can try to do the following: