Dresden 2014 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 84: Correlated Electrons: (General) Theory

TT 84.9: Talk

Thursday, April 3, 2014, 11:45–12:00, HSZ 304

Stochastic Mode Sampling (SMS) - An Efficient Approach to the Analytic Continuation Problem — •Khaldoon Ghanem and Erik Koch — Computational Materials Science, German Research School for Simulation Sciences, Jülich, Germany

Stochastic sampling methods (SSMs) provide a promising alternative to the commonly used maximum entropy method (MEM) in solving the analytic continuation problem of non-negative quantities like the spectral function or the optical conductivity. SSMs assume a flat prior probability, which is the appropriate choice in the absence of any prior knowledge, while MEM unjustifiably biases the results toward a default model. On the other hand, SSMs can be exceedingly slow compared to MEM because of the large correlation times.

We present a new stochastic sampling method, Stochastic Mode Sampling (SMS). Instead of sampling the components of the solution directly, we sample the singular vectors (modes) of the kernel, which relates the data to the solution. In this basis, the sampled quantities are uncorrelated except for the coupling through the non-negativity constraint. The weaker this coupling, the more efficient the method, so we modify the kernel such that the coupling is minimized, thus reducing correlation times dramatically in comparison to other SSMs. We also show how to make SMS solutions converge as the discretization grid becomes larger and denser.