New algorithm to enable 400+ TFlop/s sustained performance in simulations of disorder effects in high-Tc superconductors

Staggering computational and algorithmic advances in recent years now make possible systematic Quantum Monte Carlo (QMC) simulations of high temperature (high-Tc) superconductivity in a microscopic model, the two dimensional (2D) Hubbard model, with parameters relevant to the cuprate materials. Here we report the algorithmic and computational advances that enable us to study the effect of disorder and nano-scale inhomogeneities on the pair-formation and the superconducting transition temperature necessary to understand real materials. The simulation code is written with a generic and extensible approach and is tuned to perform well at scale. Significant algorithmic improvements have been made to make effective use of current supercomputing architectures. By implementing delayed Monte Carlo updates and a mixed single-/double precision mode, we are able to dramatically increase the efficiency of the code. On the Cray XT4 systems of the Oak Ridge National Laboratory (ORNL), for example, we currently run production jobs on 31 thousand processors and thereby routinely achieve a sustained performance that exceeds 200 TFlop/s. On a system with 49 thousand processors we achieved a sustained performance of 409 TFlop/s. We present a study of how random disorder in the effective Coulomb interaction strength affects the superconducting transition temperature in the Hubbard model.

[1]  K. Müller,et al.  Possible highTc superconductivity in the Ba−La−Cu−O system , 1986 .

[2]  R. Bartlett,et al.  Coupled-cluster theory in quantum chemistry , 2007 .

[3]  D. Scalapino The case for dx2 − y2 pairing in the cuprate superconductors , 1995 .

[4]  H. R. Krishnamurthy,et al.  Nonlocal Dynamical Correlations of Strongly Interacting Electron Systems , 1998 .

[5]  Mark Jarrell,et al.  Quantum Monte Carlo algorithm for nonlocal corrections to the dynamical mean-field approximation , 2001 .

[6]  M. Jarrell,et al.  Spin Susceptibility Representation of the Pairing Interaction for the two-dimensional Hubbard Model , 2007 .

[7]  J. Schrieffer,et al.  EFFECT OF FERROMAGNETIC SPIN CORRELATIONS ON SUPERCONDUCTIVITY , 1966 .

[8]  Fye,et al.  Monte Carlo method for magnetic impurities in metals. , 1986, Physical review letters.

[9]  P R C Kent,et al.  Systematic study of d-wave superconductivity in the 2D repulsive Hubbard model. , 2005, Physical review letters.

[10]  Y Ando,et al.  Inhomogeneous magnetic-field response of YBa2Cu3Oy and La2-xSrxCuO4 persisting above the bulk superconducting transition temperature. , 2008, Physical review letters.

[11]  M.Jarrell,et al.  A Quantum Monte Carlo algorithm for non-local corrections to the Dynamical Mean-Field Approximation , 2001 .

[12]  T. Maier,et al.  Dynamics of the pairing interaction in the hubbard and t-J models of high-temperature superconductors. , 2008, Physical review letters.

[13]  Zhang,et al.  Effective Hamiltonian for the superconducting Cu oxides. , 1988, Physical review. B, Condensed matter.

[14]  P. Anderson The Resonating Valence Bond State in La2CuO4 and Superconductivity , 1987, Science.

[15]  M. Jarrell,et al.  Systematic analysis of a spin-susceptibility representation of the pairing interaction in the two-dimensional Hubbard model , 2007, 0706.0241.

[16]  T. Pruschke,et al.  Quantum cluster theories , 2004, cond-mat/0404055.

[17]  Mark Jarrell,et al.  Pairing interaction in the two-dimensional Hubbard model studied with a dynamic cluster quantum Monte Carlo approximation , 2006 .

[18]  Robert A. van de Geijn,et al.  High-performance implementation of the level-3 BLAS , 2008, TOMS.