1. Multiscale methods for disordered and interacting systems. Simulations of realistic materials scale badly in the number of atoms treated explicitly, driving the need for multiscale methods which treat only the correlations between the atoms at short length scale explicitly. Correlations at longer length scales are treated at various levels of approximation.

a. Typical Medium Theory. (C. Ekuma)The coherent phase approximation [1] and its cluster extensions, including the DCA[2], fail to capture Anderson localization since they only consider averaged quantities, which ultimately feature metallic behavior. Here we extend Typical Medium Theory[3], which replaces average quantities with typical values, to its cluster version such that non-local correlations can be incorporated systematically. Our method (CTMT) opens a new avenue to study localization effect both in model and in real materials.

b. Impact of the third length scale. (Z. Meng) In multiscale methods, correlations at short length scales are treated explicitly, intermediate length scales perturbatively, and the longest length scales in a dynamical mean field. Within the dual Fermion DCA approach[4], we have included the mean field correlations for the first time. As shown in the figure, this greatly improves convergence as a function of the intermediate cluster size.

2. GPU Simulations. GPUs can be used to greatly accelerate materials simulations. By employing nearly 1000 cores they run at over 1TFLOPS.

a. GPU simulations of glasses . (S. Feng, Y. Fang, K. Tam, B. Thakur, Z. Yun, J. Ramanujam)We use parallel tempering [5] together with Multi-spin Coding [6] to perform GPU simulations of Ising glasses. The code has been verified with different temperatures and system, as shown in the figure below. With careful tuning, the performance is around 49ps/spin flip.

b. GPU enhanced quantum Monte Carlo (QMC). (C. Moore, S. Abuasal, K. Tam, B. Thakur, Z. Yun, J. Ramanujam) GPUs are ideally suited to the linear algebra inner loops of QMC simulations needed to treat the short length scales explicitly in multiscale simulations. We are developing Hirsch-Fye[8] and Continuous time [9] QMC codes that are carefully tuned for the next generation of Kepler GPUs.

3. Realistic modeling of materials. (R. Nelson).We use the density functional theory to infer the electronic structure of (Ga,Mn)As and (Ga,Mn)N and then apply a Wannier function-based downfolding method [10] to get effective Hamiltonians. Preliminary results point to significant differences between these two materials.

References

[1] R. J. Elliot et al. Rev. Mod. Phys. 46, 465 (1974); P. Soven, Phys. Rev. 156, 809 (1967).

[2] M. Jarrell et al. Phys. Rev. B 63, 125102 (2001).

[3] V. Dobrosavljević et al. Europhys.Lett.62, 76 (2003).

[4] A. N. Rubtsov, M. I. Katsnelson, and A. I. Lichtenstein, Phys. Rev. B 77,

033101 (2008). S.-X. Yang, H. Fotso, H. Hafermann, K.-M.Tam, J. Moreno, T. Pruschke, and M. Jarrell, Phys. Rev. B 84, 155106 (2011).

[5] E. Marinari and G. Parisi, “Simulated tempering: a new montecarlo scheme,” EPL (Europhysics Letters), vol. 19, p. 451, 1992; U. Hansmann, “Parallel tempering algorithm for conformational studies of biological molecules,” Chemical Physics Letters, vol. 281, no. 1-3, p. 140, 1997; Y. Sugita and Y. Okamoto, “Replica-exchange molecular dynamics method for protein folding,” Chemical Physics Letters, vol. 314, no. 1-2, p. 141, 1999; Q. Yan and J. de Pablo, “Hyperparallel tempering montecarlo simulation of polymeric systems,” The Journal of Chemical Physics, vol. 113, p. 1276, 2000.

[6] M. Creutz, L. Jacobs and C. Rebbi, Phys. Rev. Lett. 42, 1396 (1979); R. Zorn, H. J. Herrmann and C. Rebbi, Comput. Phys. Commun. 23, 337 (1981); G. O. Williams and M. H. Kalos, J. Stat. Phys. 37, 283 (1984); P. M. C. de Olivieira, Computing Boolean Statistical Models (World Scientific, 1991).

[7] Helmut G. Katzgraber,Mathias Koerner,A. P. Young: Phys. Rev. B, 73, 224432 (2006).

[8] J.E. Hirsch and R. M. FyeMonte Carlo Method for Magnetic Impurities in Metals, , Phys. Rev. Lett. 56, 2521–2524 (1986).

[9] A. N. Rubtsov,V. V. Savkin, andA. I. Lichtenstein, Continuous-time quantum Monte Carlo method for fermions, Phys. Rev. B 72, 035122 (2005)

[10] W. Ku, H. Rosner, W.E. Pickett, and R.T. Scalettar, Phys. Rev. Lett. 89, 167204-1 (2002).