1. Electronic structure calculation codes on the Asgard and Gonzales clusters Institute of Metal Physics, RAS Ural State Technical University - UPI Alexey Lukoyanov Vladimir Mazurenko Anton Kozhevnikov Prof. Vladimir Anisimov Prof. Matthias Troyer Beowulf Day, ETH Zürich 2006 Beowulf Day, ETH Zürich 2006 Institute of Metal Physics, RAS Ekaterinburg, Russia Institut für Theoretische Physik, ETH Zürich Institut für Theoretische Physik, ETH

2. Physical problem: Compounds with strongly correlated electrons LDA+U+SO * *A.O. Shorikov, A.V. Lukoyanov, M.A. Korotin, and V.I. Anisimov, Phys. Rev. B 72, 024458 (2005) Schrödinger equation LDA+DMFT (QMC) ** ** V.I. Anisimov, A.I. Poteryaev, M.A. Korotin, A.O. Anokhin, and G. Kotliar, J. Phys.: Condens. Matter 9, 7359 (1997) Dynamical mean-field theory is used to map the problem onto single-site Anderson impurity model is reduced to eigenvalue problem for trial functions 80-90 % This matrix diagonalization takes 80-90 % of the total calculation time. Gonzales facilitates us reduce calculation time deal with large compounds Gonzales facilitates us reduce calculation time substentially increase QMC statistics treat lower temperatures Solution of this impurity problem with Quantum Monte Carlo method (Hirsch-Fye method) takes > 95 % > 95 % of the total calculation time.

3. Number of processors Block sizeTotal calculation time, s Total diagonalization time, s 11×1 8×8 128×128 928.3 404.7 332.4 780.5 232.5 178.1 21×1 8×8 128×128 761.4 298.3 299.9 611.8 144.4 140.4 41×1 8×8 128×128 670.9 278.6 273.2 516.0 121.9 118.2 Parallel diagonalization of the matrix SCALAPACK and MPI for eigenvalue problem  We replaced the set of the procedure from old mathematical library by SCALAPACK procedure PZHEGVX for Hermitian matrix. For UPd 3 tests 4 procs and 128 × 128 is the best result.  Compound UPd 3 with matrix 292×292

4. Number of processors Total calculation time, s QMC simulation time, s 16923.26921.7 23523.33521.8 41850.01848.6 8975.8974.4 16542.3540.8 Parallel QMC code MPI for LDA+DMFT (QMC) method  We used MPI code to the parallel QMC simulations. For test SrVO 3 system LDA+DMFT runs more then 12 times faster.  Compound SrVO 3 with 3 degenerate orbitals and T = 1160.5 K ~ 2 h ~ 9 min

5. Plans Previous publications:  Optical conductivity of ortho-II YBa 2 Cu 3 O 6.5 E. Bascones, T.M. Rice, A.O. Shorikov, A.V. Lukoyanov, and V.I. Anisimov, Phys. Rev. B 71, 012505 (2005)  First-Order Transition between a Small Gap Semiconductor and a Ferromagnetic Metal in the Isoelectronic Alloy FeSi 1-x Ge x V.I. Anisimov, R. Hlubina, M.A. Korotin, V.V. Mazurenko, T.M. Rice, A.O. Shorikov, and M. Sigrist, Phys. Rev. Lett. 89, 257203 (2002)  Analysis of magnetic properties of (VO) 2 P 2 O 7 from Ab Initio calculations A.O. Shorikov, M. Troyer, V.V. Mazurenko, I.A. Nekrasov, V.I. Anisimov, Conference VNKSF-9, Krasnoyarsk, Russia (2003). 1.Continue development and optimization of our LDA+U+SO and LDA+DMFT (QMC) codes 2. Use Gonzales cluster for the electronic structure calculations of strongly correlated compounds, e.g., (VO) 2 P 2 O 7 etc. 3. Collaboration with the ALPS project http://alps.comp-phys.org