Improved real-time dynamics from imaginary frequency lattice simulations

TL;DR

This paper introduces a novel imaginary frequency simulation approach that enhances the reconstruction of real-time spectral functions in quantum field theories, addressing the ill-posed inverse problem more effectively.

Contribution

The authors develop a new simulation prescription in imaginary frequencies that improves the resolution of spectral functions, especially between specific frequency ranges, in lattice quantum field theory.

Findings

Enhanced spectral function reconstruction in a 0+1D scalar model.

Better resolution of correlation functions outside Matsubara frequencies.

Significant improvements due to the rational kernel in imaginary frequencies.

Abstract

The computation of real-time properties, such as transport coefficients or bound state spectra of strongly interacting quantum fields in thermal equilibrium is a pressing matter. Since the sign problem prevents a direct evaluation of these quantities, lattice data needs to be analytically continued from the Euclidean domain of the simulation to Minkowski time, in general an ill-posed inverse problem. Here we report on a novel approach to improve the determination of real-time information in the form of spectral functions by setting up a simulation prescription in imaginary frequencies. By carefully distinguishing between initial conditions and quantum dynamics one obtains access to correlation functions also outside the conventional Matsubara frequencies. In particular the range between $\omega_0$ and $\omega_1=2\pi T$, which is most relevant for the inverse problem may be more highly resolved. In combination with the fact that in imaginary frequencies the kernel of the inverse problem is not an exponential but only a rational function we observe significant improvements in the reconstruction of spectral functions, demonstrated in a simple 0+1 dimensional scalar field theory toy model.