Now, looking at D, instead of M N initial terms, there are χ χ 2 ⋅ ⋅ M ( N − − 2 ) + 2 χ χ M + ( N − − 1 ) χ χ . Apparently this is just a fancy way of rewriting the coefficients c i 1 i 2 . . i N , but in fact there is more to it than that. Assuming that N is even, the Schmidt rank χ χ for a bipartite cut in the middle of the chain can have a maximal value of M N / 2 ; in this case we end up with at least M N + 1 ⋅ ⋅ ( N − − 2 ) coefficients, considering only the χ χ 2 ones, slightly more than the initial M N ! The truth is that the decomposition D is useful when dealing with systems that exhibit a low degree of entanglement, which fortunately is the case with many 1D systems, where the Schmidt coefficients of the ground state decay in an exponential manner with α α :