 Apparently this is just a fancy way of rewriting the coefficients formula_33, but in fact there is more to it than that.Assuming that "N" is even, the Schmidt rank formula_26 for a bipartite cut in the middle of the chain can have a maximal value of formula_35; in this case we end up with at least formula_36 coefficients, considering only the formula_37 ones, slightly more than the initial formula_31!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 formula_39