Slater hull necessary conditions

C. Necessary Conditions from the Slater Hull (R, R) Conditions... 

Necessary conditions based on the Slater hull have been pursued by Kummer, McRae and Davidson, Yoseloff and Kuhn, and Deza and Laurent, among others [24-26, 29, 42-44]. 

As previously discussed, when developing necessary conditions for N-representability, it is useful to consider the subset of Hamiltonians whose ground-state energy is zero. Applying this idea to the Slater hull, the following Hamiltonians arise as important constraints ... 

The Slater hull constraints represent the entire family of A -representabUity constraints that can be expressed using only the diagonal elements of the reduced density matrix [25, 43]. That is, the complete set of (g, K) conditions is necessary and sufficient to ensure the A -representability of the g-density. 

Because the Slater hull constraints are insufficient to ensure A -representability, it is important to find additional methods for constraining the off-diagonal elements of the density matrix. Obtaining constraints that supersede the Slater hull requires considering Hamiltonians with a more general form than polynomials of number operators. As discussed in Section UFA, matters are especially simple if the Hamiltonian has nonnegative eigenvalues, because then the necessary conditions for A-representability take the form... 

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