title: Large-scale semidefinite programming for many-electron quantum mechanics.
abstract: The energy of a many-electron quantum system can be approximated by a constrained optimization of the two-electron reduced density matrix (2-RDM) that is solvable in polynomial time by semidefinite programming (SDP). Here we develop a SDP method for computing strongly correlated 2-RDMs that is 10-20 times faster than previous methods [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)]. We illustrate with (i) the dissociation of N(2) and (ii) the metal-to-insulator transition of H(50). For H(50) the SDP problem has 9.4×10(6) variables. This advance also expands the feasibility of large-scale applications in quantum information, control, statistics, and economics.
authors.affiliation: Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA. damazz@uchicago.edu
authors.forename: David A
authors.initials: DA
authors.lastname: Mazziotti