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.
Figure 1 The hybridization function, (𝜔), is the
order parameter for the localization
transition. It goes to zero at the critical
disorder strength Vc. Above Vc, electrons
become localized in the within the length scale
of the cluster
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.
Figure 2 Convergence of the antiferromagnetic leading
eigenvalue in the 2D Hubbard model. The results
obtained from the multi-scale approach converge faster
than that obtained from the two length scale approach.
2. GPU Simulations. GPUs can be used to greatly
accelerate materials simulations. By employing
nearly 1000 cores they run at over 1TFLOP.
a. GPU simulations of glasses . (S. Feng) 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. The performance is around 55ps/spin flip.
b. GPU enhanced quantum Monte Carlo (QMC). (C.
Moore) GPUs are ideally suited to the linear algebra
inner loops of QMC simulations needed to treat the
short length scales explicitly in multiscale simulations.
Figure 3 Binder Ratio vs Beta, compared with
published results [7]
We are developing Hirsch-Fye[8] and Continuous time [9] QMC codes that are 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.
Figure 4. Mn d-character of polarized
(GaMn)As (left panel) and (GaMn)N
(right) electronic bands. The occupied dlike band in (GaMn)As is located
around -5 eV, while holes have As p-like
character. However, in (GaMn)N dorbitals hybridize strongly with N p-like
orbitals. This strong hybridization
results in a strong fluctuation of the
local charge and spin density of Mn.
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