New Frontiers in Quantum Many-Body Problems Using State-of-the-Art Semidefinite Programming Algorithms

Jeff Hammond, University of Chicago

The variational reduced-density-matrix (RDM) method has recently been applied to two difficult problems in quantum many-body theory: (1) the ab-initio calculation of open-shell molecules, and (2) the Hubbard model. In (1) the method is shown to be as accurate as coupled-cluster methods without the introduction of spin-contamination. The non-perturbative calculations of (2) are matched in accuracy only by numerically exact methods, which have significant computational cost. In both examples, a state-of-the-art semidefinite programming algorithm developed by Mazziotti was used to solve these problems using very modest computational resources. The extension of this method to even more challenging problems will be discussed.

Abstract Author(s): Jeff R. Hammond and David A. Mazziotti