Jan 282012

A very interesting paper on an algebraic operator approach to electronic structure by Neil Shenvi and Weitao Yang appeared recently in the Journal of Chemical Physics.  The authors use Jordan algebras to compute the eigenvalues of a second quantized Hamiltonian.  The major result presented in the paper relates the lowest eigenvalue of the Hamiltonian to the lowest eigenvalue of the structure factor matrix \epsilon_{ik} defined by the equation  \{\hat{A}_i,\hat{H}\}  = \sum_k \epsilon_{ik} \hat{A}_k. Here the operators \hat{A}_i form a set that is closed under multiplication with \hat{H}.  Of course the rank of the many-body operators \hat{A}_i spans the entire Fock space and therefore for this approach to be viable it is necessary to find a way to approximate higher-rank operators with low-rank ones.  Shenvi and Yang propose here to use an operator decomposition in conjunction with an ansatz for the operators \hat{A}_i that contains at most two-body terms.  Preliminary results for the Hubbard model look promising, especially considering that with the approximations introduced in the paper the overall scaling of this approach is cubic in the number of basis functions.  The paper is a good read and has a contagious enthusiasm.

 January 28, 2012  Article review

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