Electronic structure calculation codes

1
Institut für Theoretische Physik, ETH
Institute of Metal Physics, RASUral State
Technical University - UPI
Electronic structure calculation codes on the
Asgard and Gonzales clusters
Alexey Lukoyanov Vladimir Mazurenko Anton
Kozhevnikov Prof. Vladimir Anisimov Prof.
Matthias Troyer
Institute of Metal Physics, RAS Ekaterinburg,
Russia Institut für Theoretische Physik, ETH
Zürich
Beowulf Day, ETH Zürich 2006
2
Physical problemCompounds with strongly
correlated electrons
LDAUSO
LDADMFT (QMC)
Schrödinger equation
Dynamical mean-field theory is used to map the
problem onto single-site Anderson impurity model

for trial functions
is reduced to eigenvalue problem
Solution of this impurity problem with Quantum
Monte Carlo method (Hirsch-Fye method) takes gt
95 of the total calculation time.
This matrix diagonalization takes 80-90 of the
total calculation time.

• Gonzales facilitates us
• reduce calculation time
• substentially increase QMC statistics
• treat lower temperatures

• Gonzales facilitates us
• reduce calculation time
• deal with large compounds

A.O. Shorikov, A.V. Lukoyanov, M.A. Korotin,
and V.I. Anisimov, Phys. Rev. B 72, 024458
(2005)
V.I. Anisimov, A.I. Poteryaev, M.A. Korotin,
A.O. Anokhin, and G. Kotliar, J. Phys. Condens.
Matter 9, 7359 (1997)
3
Parallel diagonalization of the matrixSCALAPACK
and MPI for eigenvalue problem

• Compound UPd3 with matrix 292292

Number of processors Block size Total calculation time, s Total diagonalization time, s
1 11 88 128128 928.3 404.7 332.4 780.5 232.5 178.1
2 11 88 128128 761.4 298.3 299.9 611.8 144.4 140.4
4 11 88 128128 670.9 278.6 273.2 516.0 121.9 118.2
We replaced the set of the procedure from old
mathematical library by SCALAPACK procedure
PZHEGVX for Hermitian matrix. For UPd3 tests 4
procs and 128128 is the best result.
?
4
Parallel QMC code MPI for LDADMFT (QMC) method

• Compound SrVO3 with 3 degenerate orbitals and T
  1160.5 K

Number of processors Total calculation time, s QMC simulation time, s
1 6923.2 6921.7
2 3523.3 3521.8
4 1850.0 1848.6
8 975.8 974.4
16 542.3 540.8
2 h
9 min
?
We used MPI code to the parallel QMC
simulations. For test SrVO3 system LDADMFT runs
more then 12 times faster.
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Plans

• Continue development and optimization of our
• LDAUSO and LDADMFT (QMC) codes
• 2. Use Gonzales cluster for the electronic
  structure calculations
• of strongly correlated compounds, e.g.,
  (VO)2P2O7 etc.
• 3. Collaboration with the ALPS project
  http//alps.comp-phys.org

• Previous publications
• Optical conductivity of ortho-II YBa2Cu3O6.5 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 FeSi1-xGex 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)2P2O7
  from Ab Initio calculations
• A.O. Shorikov, M. Troyer, V.V. Mazurenko, I.A.
  Nekrasov, V.I. Anisimov, Conference VNKSF-9,
  Krasnoyarsk, Russia (2003).