Physical insights from imaginary-time density--density correlation functions

TL;DR

This paper demonstrates that imaginary-time density--density correlation functions contain all the physical information of dynamic structure factors, allowing direct extraction of physical properties without analytic continuation, with applications to quantum many-body systems like the uniform electron gas.

Contribution

It introduces a method to directly analyze imaginary-time correlation functions to obtain physical insights, bypassing the difficult analytic continuation process.

Findings

Key physical information can be extracted directly from $F(q,\tau)$.

The method applies to systems like the uniform electron gas.

Features like the roton minimum are visible in $F(q,\tau)$.

Abstract

The accurate theoretical description of the dynamic properties of correlated quantum many-body systems such as the dynamic structure factor $S(\mathbf{q},\omega)$ constitutes an important task in many fields. Unfortunately, highly accurate quantum Monte Carlo methods are usually restricted to the imaginary time domain, and the analytic continuation of the imaginary time density--density correlation function $F(\mathbf{q},\tau)$ to real frequencies is a notoriously hard problem. In this work, we argue that no such analytic continuation is required as $F(\mathbf{q},\tau)$ contains, by definition, the same physical information as $S(\mathbf{q},\omega)$, only in an unfamiliar representation. Specifically, we show how we can directly extract key information such as the temperature or quasi-particle excitation energies from the $\tau$-domain, which is highly relevant for equation-of-state measurements of matter under extreme conditions. As a practical example, we consider \emph{ab initio} path integral Monte Carlo results for the uniform electron gas (UEG), and demonstrate that even nontrivial processes such as the \emph{roton feature} of the UEG at low density straightforwardly manifest in $F(\mathbf{q},\tau)$. In fact, directly working in the $\tau$-domain is advantageous for many reasons and holds the enticing promise for unprecedented agreement between theory and experiment.