Doctor of Philosophy (PhD)
Physics and Astronomy
We study the Edwards-Anderson model on a simple cubic lattice with a finite constant external field. We employ an indicator composed of a ratio of susceptibilities at finite momenta, which was recently proposed to avoid the difficulties of a zero momentum quantity, for capturing the spin glass phase transition. Unfortunately, this new indicator is fairly noisy, so a large pool of samples at low temperature and small external field are needed to generate results with a sufficiently small statistical error for analysis. We thus implement the Monte Carlo method using graphics processing units to drastically speed up the simulation. We confirm previous findings that conventional indicators for the spin glass transition, including the Binder ratio and the correlation length do not show any indication of a transition for rather low temperatures. However, the ratio of spin glass susceptibilities does show crossing behavior, albeit a systematic analysis is beyond the reach of the present data. This reveals the difficulty with current numerical methods and computing capability in studying this problem. One of the fundamental challenges of theoretical condensed matter physics is the accurate solution of quantum impurity models. By taking expansion in the hybridization about an exactly solved local limit, one can formulate a quantum impurity solver. We implement the hybridization expansion quantum impurity solver on Intel Xeon Phi accelerators, and aim to apply this approach on the Dynamic Hubbard Models.
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Feng, Sheng, "Study of Condensed Matter Systems with Monte Carlo Simulation on Heterogeneous Computing Systems" (2016). LSU Doctoral Dissertations. 3741.