# Probing transport in quantum many-fermion simulations via quantum loop topography

## TL;DR

This paper introduces quantum loop topography (QLT), a machine learning method that directly probes transport properties in quantum many-fermion systems, enabling detection of complex phenomena like superconducting fluctuations and non-Fermi liquids.

## Contribution

The authors develop and demonstrate a novel QLT-based machine learning approach to analyze transport in quantum many-fermion models, providing a new tool for studying elusive transport phenomena.

## Key findings

- QLT detects transport changes consistent with phase diagrams.
- Successfully applied to negative-U Hubbard and spin-fermion models.
- Potential to identify non-Fermi liquids and other complex states.

## Abstract

Quantum many-fermion systems give rise to diverse states of matter that often reveal themselves in distinctive transport properties. While some of these states can be captured by microscopic models accessible to numerical exact quantum Monte Carlo simulations, it nevertheless remains challenging to numerically access their transport properties. Here we demonstrate that quantum loop topography (QLT) can be used to directly probe transport by machine learning current-current correlations in imaginary time. We showcase this approach by studying the emergence of superconducting fluctuations in the negative-U Hubbard model and a spin-fermion model for a metallic quantum critical point. For both sign-free models, we find that the QLT approach detects a change in transport in very good agreement with their established phase diagrams. These proof-of-principle calculations combined with the numerical efficiency of the QLT approach point a way to identify hitherto elusive transport phenomena such as non-Fermi liquids using machine learning algorithms.