Thermal dynamics on the lattice with exponentially improved accuracy

TL;DR

This paper introduces a new lattice simulation method for thermal quantum fields that directly accesses correlation functions outside traditional frequency ranges, significantly enhancing the accuracy of spectral function reconstruction.

Contribution

It proposes a novel simulation approach in imaginary frequency space that improves the resolution of thermal spectral functions beyond conventional methods.

Findings

Accurately captures spectral features previously inaccessible in Euclidean simulations

Demonstrates exponential improvement in unfolding spectral functions

Validates method with a 0+1-dimensional scalar field theory

Abstract

We present a novel simulation prescription for thermal quantum fields on a lattice that operates directly in imaginary frequency space. By distinguishing initial conditions from quantum dynamics it provides access to correlation functions also outside of the conventional Matsubara frequencies $\omega_n=2\pi n T$. In particular it resolves their frequency dependence between $\omega=0$ and $\omega_1=2\pi T$, where the thermal physics $\omega\sim T$ of e.g.~transport phenomena is dominantly encoded. Real-time spectral functions are related to these correlators via an integral transform with rational kernel, so their unfolding is exponentially improved compared to Euclidean simulations. We demonstrate this improvement within a $0+1$-dimensional scalar field theory and show that spectral features inaccessible in standard Euclidean simulations are quantitatively captured.