Berlin 2015 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 112: Correlated Electrons: (General) Theory 3

TT 112.9: Vortrag

Freitag, 20. März 2015, 11:45–12:00, H 3010

Analytic Continuation Using Stochastic Sampling - Efficient Sampling, Functional Reformulation and Parameter Selection — •Khaldoon Ghanem and Erik Koch — German Research School for Simulation Sciences, Jülich, Germany

The stochastic sampling method (StochS) is used for the analytic continuation of quantum Monte Carlo data from the imaginary axis to the real axis. Compared to the maximum entropy method (MaxEnt), StochS does not have explicit parameters, and it has the potential for resolving sharp features in the spectrum.

We present a new efficient algorithm for performing StochS called Blocked Mode Sampling (BMS). In comparison to earlier StochS methods, BMS reduces the computational times by orders of magnitude. We find that StochS results depend on the discretization, an effect which has not been discussed before in the literature. We show that the grid dependence implies a default model and that by reformulating the method in function space, we can make the default model explicit and get grid-independent results. Demanding proper functional Bayesian formulation of any analytic continuation method excludes MaxEnt and Tikhonov regularization. Therefore, StochS is currently the only available Bayesian method and is actually one of the simplest methods with minimal parameters. Finally, we present guidelines for choosing the default model of StochS and its grid. This gives good results in practice and can be used as a starting point for a more rigorous treatment in the future.