Maximum quantum entropy method
Jae-Hoon Sim,Myung Joon Han +1 more
TL;DR: In this article, a maximum entropy method for analytic continuation is extended by introducing quantum relative entropy, which is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input matrix.
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Abstract: A maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input matrix. As a result, the continuation of off-diagonal elements becomes straightforward. Without introducing any further ambiguity, the Bayesian probabilistic interpretation is maintained just as in the conventional maximum entropy method. The applications of our generalized formalism to a model spectrum and a real material demonstrate its usefulness and superiority.
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Citations
Nevanlinna Analytical Continuation.
TL;DR: It is shown that explicitly respecting the analytic "Nevanlinna" structure of the Green's function leads to intrinsically positive and normalized spectral functions, and a continued fraction expansion that yields all possible functions consistent with the analytic structure is presented.
95
Analytic continuation via domain knowledge free machine learning
TL;DR: The machine-learning-based approach to analytic continuation not only provides the more accurate spectrum than the conventional methods in terms of peak positions and heights, but is also more robust against the noise which is the required key feature for any continuation technique to be successful.
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Effective J = 1/2 insulating state in Ruddlesden-Popper iridates: An LDA+DMFT study
TL;DR: In this paper, the authors investigated the metal-insulator transition across the Ruddlesden-Popper (RP) series of iridates and explored the robustness of the ${J}{\mathrm{eff}}=1/2$ state against band effects due to itineracy, tetragonal distortion, octahedral rotation, and Coulomb interaction.
Analytical continuation of matrix-valued functions: Carathéodory formalism
TL;DR: In this paper, the authors derived the criteria under which such functions exist for given Matsubara data and presented an interpolation algorithm that intrinsically respects their mathematical properties, and showed that the continuation exactly recovers all off-diagonal and diagonal elements.
56
•Posted Content
ana_cont: Python package for analytic continuation
Josef Kaufmann,Karsten Held +1 more
TL;DR: In this article, the authors present the Python package ana_cont for the analytic continuation of fermionic and bosonic many-body Green's functions by means of either the Pade approximants or the maximum entropy method.
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The ground state of the electron gas by a stochastic method
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