Stochastic Analytic Continuation: A Bayesian Approach

Ghanem, Khaldoon

Dissertation / PhD Thesis

FZJ-2017-07845

Stochastic Analytic Continuation: A Bayesian Approach

Ghanem, K. (Corresponding author)FZJ*

2017

183 p. (2017) = Dissertation, RWTH Aachen University, 2017

Please use a persistent id in citations: http://hdl.handle.net/2128/15995

Abstract: 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, StochS does not have explicit parameters, and one would expect the results to be unbiased. We present a very efficient algorithm for performing StochS and use it to study the effect of the discretization grid. Surprisingly, we find that the grid affects the results of StochS acting as an implicit default model. We provide a recipe for choosing a reliable StochS grid.To reduce the effect of the grid, we extend StochS into a gridless method (gStochS) by sampling the grid points from a default model instead of having them fixed. The effect of the default model is much reduced in gStochS compared to StochS and depends mainly on its width rather than its shape. The proper width can then be chosen using a simple recipe like we did in StochS.Finally, to avoid fixing the width, we go one step further and extend gStochS to sample over a whole class of default models with different widths. The extended method (eStochS) is then able to automatically relocate the grid points and concentrate them in the important region. Test cases show that eStochS gives good results resolving sharp features in the spectrum without the need for fine tuning a default model.

Note: Dissertation, RWTH Aachen University, 2017

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