Extracting the field theory description of a quantum many-body system from experimental data

TL;DR

This paper presents a method to derive quantum field theory descriptions directly from experimental data in quantum many-body systems, demonstrated through a quantum simulation of the sine-Gordon model.

Contribution

It introduces a novel approach to extract irreducible quantum field theory components from experimental correlation data, enabling direct analysis of complex quantum systems.

Findings

Successfully extracted 1PI vertices from experimental data

Verified the method by comparing with theoretical estimates

Demonstrated the approach on a quantum simulation of the sine-Gordon model

Abstract

Quantum field theory is a powerful tool to describe the relevant physics governing complex quantum many-body systems. Here we develop a general pathway to extract the irreducible building blocks of quantum field theoretical descriptions and its parameters purely from experimental data. This is accomplished by extracting the one-particle irreducible (1PI) vertices from which one can construct all observables. To match the capabilities of experimental techniques used in quantum simulation experiments, our approach employs a formulation of quantum field theory based on equal-time correlation functions only. We illustrate our procedure by applying it to the quantum sine-Gordon model in thermal equilibrium. The theoretical foundations are illustrated by estimating the irreducible vertices at equal times both analytically and using numerical simulations. We then demonstrate explicitly how to extract these quantities from an experiment where we quantum simulate the sine-Gordon model by two tunnel-coupled superfluids. We extract the full two-point function and the interaction vertex (four-point function) and their variation with momentum, encoding the `running' of the couplings. The measured 1PI vertices are compared to the theoretical estimates, verifying our procedure. Our work opens new ways of addressing fundamental questions in quantum field theory, which are relevant in high-energy and condensed matter physics, and in taking quantum phenomena from fundamental science to practical technology.