Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo data

Abstract

A new approach of solving the ill-conditioned inverse problem for analytical continuation is proposed. The root of the problem lies in the fact that even tiny noise of imaginary-time input data has a serious impact on the inferred real-frequency spectra. By means of a modern regularization technique, we eliminate redundant degrees of freedom that essentially carry the noise, leaving only relevant information unaffected by the noise. The resultant spectrum is represented with minimal bases and thus a stable analytical continuation is achieved. This framework further provides a tool for analyzing to what extent the Monte Carlo data need to be accurate to resolve details of an expected spectral function.

7 pages, 5 figures

References in corpus (10)

• Continuous-time Monte Carlo methods for quantum impurity models
• Fractional excitations in the square-lattice quantum antiferromagnet
• Numerical analytic continuation: Answers to well-posed questions
• Analytical continuation of imaginary axis data using maximum entropy
• Statistical and computational intelligence approach to analytic continuation in Quantum Monte Carlo
• One particle spectral function and analytic continuation for many-body implementation in the EMTO method
• Fast and Efficient Stochastic Optimization for Analytic Continuation
• Detection of cheating by decimation algorithm
• Extracting spectral properties from Keldysh Green functions
• Projected Regression Methods for Inverting Fredholm Integrals: Formalism and Application to Analytical Continuation

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