Efficiently generalizing ultra-cold atomic simulations via inhomogeneous dynamical mean-field theory from two-to three-dimensions

J. K. Freericks, H. R. Krishnamurthy, P. Carrier, Yousef Saad

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

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 languageEnglish (US)
Title of host publicationProceedings - 2010 DoD High Performance Computing Modernization Program Users Group Conference, HPCMP UGC 2010
Pages221-227
Number of pages7
DOIs
StatePublished - Oct 5 2011
Event2010 DoD High Performance Computing Modernization Program Users Group Conference, HPCMP UGC 2010 - Schaumburg, IL, United States
Duration: Jun 14 2010Jun 17 2010

Other

Other2010 DoD High Performance Computing Modernization Program Users Group Conference, HPCMP UGC 2010
CountryUnited States
CitySchaumburg, IL
Period6/14/106/17/10

Keywords

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

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