## Abstract

We describe techniques that we are implementing to move inhomogeneous dynamical mean-field theory simulations from two-to three-dimensions. Two-dimensional simulations typically run on 2,000-10,000 lattice sites, while three-dimensional simulations typically need to run on 1,000,000 or more lattice sites. The inhomogeneous dynamical mean-field theory requires the diagonal of the inverse of many sparse matrices with the same sparsity pattern, and a dimension equal to the number of lattice-sites. For two-dimensional systems, we have employed general dense LAPACK routines since the matrices are small enough. For three-dimensional systems, we need to employ sparse matrix techniques. Here, we present one possible strategy for the sparse matrix routine, based on the well-known Lanczos technique, with a long run of the algorithm and (partial) reorthogonalization. This approach is about two-times faster than the LAPACK routines with identical accuracy, and hence will become the standard we use on the two-dimensional problems. We illustrate this approach on the problem of increasing the efficiency for pre-forming dipolar molecules in K-Rb mixtures on a lattice. We compare the local density approximation to inhomogeneous dynamical mean-field theory to illustrate how the local density approximation fails at low-temperature, and to illustrate the benefits of the new algorithms. For a three-dimensional problem, a speed-up of 1,000 or more times is needed. We end by discussing some options that are promising toward reaching this goal.

Original language | English (US) |
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Title of host publication | Proceedings - 2010 DoD High Performance Computing Modernization Program Users Group Conference, HPCMP UGC 2010 |

Pages | 221-227 |

Number of pages | 7 |

DOIs | |

State | Published - Oct 5 2011 |

Event | 2010 DoD High Performance Computing Modernization Program Users Group Conference, HPCMP UGC 2010 - Schaumburg, IL, United States Duration: Jun 14 2010 → Jun 17 2010 |

### Other

Other | 2010 DoD High Performance Computing Modernization Program Users Group Conference, HPCMP UGC 2010 |
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Country | United States |

City | Schaumburg, IL |

Period | 6/14/10 → 6/17/10 |

## Keywords

- Bose atoms
- Inhomogeneous dynamical mean-field theory
- mxitures of Fermi
- preforming dipolar matter