Minimal Pole Representation and Controlled Analytic Continuation of Matsubara Response Functions

Abstract

Analytical continuation is a central step in the simulation of finite-temperature field theories in which numerically obtained Matsubara data is continued to the real frequency axis for physical interpretation. Numerical analytic continuation is considered to be an ill-posed problem where uncertainties on the Matsubara axis are aplified exponentially. Here, we present a systematic and controlled procedure that approximates any Matsubara function by a minimal pole representation to within a predefined precision. We then show systematic convergence to the exact spectral function on the real axis as a function of our control parameter for a range of physically relevant setups. Our methodology is robust to noise and paves the way towards reliable analytic continuation in many-body theory and, by providing access to the analytic structure of the functions, direct theoretical interpretation of physical properties.

References in corpus (10)

• Continuous-time Monte Carlo methods for quantum impurity models
• Updated Core Libraries of the ALPS Project
• Antiferromagnetism and the gap of a Mott insulator: Results from analytic continuation of the self-energy
• Numerical analytic continuation: Answers to well-posed questions
• Analytical Continuation of Matrix-Valued Functions: Carathéodory Formalism
• Pairing Glue in the Two Dimensional Hubbard Model
• Bosonic Nevanlinna Analytic Continuation
• One particle spectral function and analytic continuation for many-body implementation in the EMTO method
• Maximum entropy analytic continuation for frequency-dependent transport coefficients with non-positive spectral weight
• Analytic continuation with Padé decomposition

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