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.
Keywords
Cite
@article{arxiv.2312.10576,
title = {Minimal Pole Representation and Controlled Analytic Continuation of Matsubara Response Functions},
author = {Lei Zhang and Emanuel Gull},
journal= {arXiv preprint arXiv:2312.10576},
year = {2024}
}