Parameter-free analytic continuation for quantum many-body calculations

TL;DR

This paper introduces a parameter-free analytic continuation method for quantum many-body calculations that reliably estimates spectral functions from imaginary-time data without needing prior parameters.

Contribution

The authors develop a novel, parameter-free analytic continuation technique utilizing a kernel grid, causal spline, and L-curve criterion, with bootstrap averaging for improved statistical handling.

Findings

Spectral functions converge systematically to exact results as statistical errors decrease.

The method successfully identifies non-Fermi liquid behavior near half filling in the Hubbard model.

It provides a reliable tool for analyzing imaginary-time quantum many-body data.

Abstract

We develop a reliable parameter-free analytic continuation method for quantum many-body calculations. Our method is based on a kernel grid, a causal spline, a regularization using the second-derivative roughness penalty, and the L-curve criterion. We also develop the L-curve averaged deviation to estimate the precision of our analytic continuation. To deal with statistically obtained data more efficiently, we further develop a bootstrap-averaged analytic continuation method. In the test using the exact imaginary-frequency Green's function with added statistical error, our method produces the spectral function that converges systematically to the exact one as the statistical error decreases. As an application, we simulate the two-orbital Hubbard model for various electron numbers with the dynamical-mean field theory in the imaginary time and obtain the real-frequency self-energy with our analytic continuation method, clearly identifying a non-Fermi liquid behavior as the electron number approaches the half filling from the quarter filling. Our analytic continuation can be used widely and it will facilitate drawing clear conclusions from imaginary-time quantum many-body calculations.