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arXiv:cond-mat/9503098 · Journal of Physics Condensed Matter

Consistent application of maximum entropy to quantum Monte Carlo data

Wolfgang von der Linden, R. Preuss, Werner R. Hanke

Published May 20, 1996• 7 citations
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Abstract

Bayesian probability theory along with the maximum entropy concept is widely used for inferential problems, particularly to infer dynamic properties of strongly correlated fermion systems from quantum Monte Carlo (QMC) imaginary time data. In current QMC applications, however, the error covariance of the QMC data is not treated consistently. Here we present a consistent Bayesian analysis of all the information provided by the QMC simulation. This approach allows us to infer reliable results with the least amount of computer time.

DOI
10.1088/0953-8984/8/21/013

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Bayesian probability theory along with the maximum entropy concept is widely used for inferential problems, particularly to infer dynamic properties of strongly correlated fermion systems from quantum Monte Carlo (QMC) imaginary time data. In current QMC applications, however, the error covariance of the QMC data is not treated consistently. Here we present a consistent Bayesian analysis of all the information provided by the QMC simulation. This approach allows us to infer reliable results with the least amount of computer time.
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An outstanding problem in the simulation of condensed matter phenomena is how to obtain dynamical information. We consider the numerical analytic continuation of imaginary time Quantum Monte Carlo data to obtain real frequency spectral functions. We suggest an image reconstruction approach which has been widely applied to data analysis in experimental research, the Maximum Entropy Method (MaxEnt). We report encouraging preliminary results for the Fano-Anderson model of an impurity state in a continuum. The incorporation of additional prior information, such as sum rules and asymptotic behavior, can be expected to significantly improve results. We also compare MaxEnt to alternative methods. 17 refs., 4 figs.
We describe a method of obtaining thermodynamic properties of quantum systems using Bayesian inference maximum entropy techniques. The method is applicable to energy values sampled at a discrete set of temperatures from quantum Monte Carlo simulations. The internal energy and the specific heat of the system are easily obtained as are errorbars on these quantities. The entropy and the free energy are also obtainable. No assumptions as to the specific functional form of the energy are made. The use of a priori information, such as a sum rule on the entropy, is built into the method. As a nontrivial example of the method, we obtain the specific heat of the three-dimensional periodic Anderson model.