Bayesian parametric analytic continuation of Green's functions

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

Abstract

Bayesian parametric analytic continuation (BPAC) is proposed for the analytic continuation of noisy imaginary-time Green’s function data as, e.g., obtained by continuous-time quantum Monte Carlo simulations (CTQMC). Within BPAC, the spectral function is inferred from a suitable set of parametrized basis functions. Bayesian model comparison then allows to assess the reliability of different parametrizations. The required evidence integrals of such a model comparison are determined by nested sampling. Compared to the maximum entropy method (MEM), routinely used for the analytic continuation of CTQMC data, the presented approach allows to infer whether the data support specific structures of the spectral function. We demonstrate the capability of BPAC in terms of CTQMC data for an Anderson impurity model (AIM) that shows a generalized Kondo scenario and compare the BPAC reconstruction to the MEM as well as to the spectral function obtained from the real-time fork tensor product state impurity solver where no analytic continuation is required. Furthermore, we present a combination of MEM and BPAC and its application to an AIM arising from the ab initio treatment of SrVO3 .
Originalspracheenglisch
Aufsatznummer075137
FachzeitschriftPhysical Review / B
Jahrgang100
Ausgabenummer7
DOIs
PublikationsstatusVeröffentlicht - 19 Aug 2019

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Maximum entropy methods
Green's function
maximum entropy method
Green's functions
data simulation
Impurities
impurities
forks
time functions
Tensors
sampling
tensors
Sampling
products
Monte Carlo simulation
simulation

Dies zitieren

Bayesian parametric analytic continuation of Green's functions. / Rumetshofer, Michael; Bauernfeind, Daniel; von der Linden, Wolfgang.

in: Physical Review / B, Jahrgang 100, Nr. 7, 075137, 19.08.2019.

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

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AB - Bayesian parametric analytic continuation (BPAC) is proposed for the analytic continuation of noisy imaginary-time Green’s function data as, e.g., obtained by continuous-time quantum Monte Carlo simulations (CTQMC). Within BPAC, the spectral function is inferred from a suitable set of parametrized basis functions. Bayesian model comparison then allows to assess the reliability of different parametrizations. The required evidence integrals of such a model comparison are determined by nested sampling. Compared to the maximum entropy method (MEM), routinely used for the analytic continuation of CTQMC data, the presented approach allows to infer whether the data support specific structures of the spectral function. We demonstrate the capability of BPAC in terms of CTQMC data for an Anderson impurity model (AIM) that shows a generalized Kondo scenario and compare the BPAC reconstruction to the MEM as well as to the spectral function obtained from the real-time fork tensor product state impurity solver where no analytic continuation is required. Furthermore, we present a combination of MEM and BPAC and its application to an AIM arising from the ab initio treatment of SrVO3 .

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