|About this Abstract
||2016 TMS Annual Meeting & Exhibition
||Computational Materials Discovery and Optimization: From 2D to Bulk Materials
||Proving the Exact Ground State of a Generalized Ising Model by Convex Optimization and MAX-SAT
||Wenxuan Huang, Daniil Kitchaev, Stephen Dacek, Ziqin Rong, Alexander Urban, Alexander Toumar, Shan Cao, Chuan Luo, Gerbrand Ceder
|On-Site Speaker (Planned)
We present an algorithm to find exact ground states of lattice models, a fundamental problem in condensed matter and materials theory. The algorithm not only finds the ground state but also proves that it is an absolute minimum. Combinatorial optimization (MAX-SAT) and non-smooth convex optimization (MAX-MIN) are combined to provide upper and lower bounds respectively on the ground state energy. By systematically converging upper and lower bounds to each other, we find and prove the exact ground state for realistic Hamiltonians whose solutions are otherwise intractable via traditional methods.
Our algorithm is the first general and scalable method for finding provable global energy minima of lattice Hamiltonians. Considering that currently such Hamiltonians are solved using simulated annealing and genetic algorithms that are often unable to find the true global energy minimum, our work opens the door to resolving long-standing uncertainties in lattice models of physical phenomena.
||Planned: A print-only volume