# Quantifying the effect of interactions in quantum many-body systems

## TL;DR

This paper reviews the concept of interaction distance as a systematic tool to quantify and diagnose the effects of interactions in quantum many-body systems, illustrated through a Fermi-Hubbard dimer example.

## Contribution

It introduces and explains the interaction distance method for analyzing the impact of interactions on quantum systems, providing a pedagogical overview and practical illustration.

## Key findings

- Interaction distance quantifies the effect of interactions on energy spectra.
- It serves as a diagnostic tool for emergent physics in many-body systems.
- Demonstrated on a 1D Fermi-Hubbard dimer.

## Abstract

Free fermion systems enjoy a privileged place in physics. With their simple structure they can explain a variety of effects, ranging from insulating and metallic behaviours to superconductivity and the integer quantum Hall effect. Interactions, e.g. in the form of Coulomb repulsion, can dramatically alter this picture by giving rise to emerging physics that may not resemble free fermions. Examples of such phenomena include high-temperature superconductivity, fractional quantum Hall effect, Kondo effect and quantum spin liquids. The non-perturbative behaviour of such systems remains a major obstacle to their theoretical understanding that could unlock further technological applications. Here, we present a pedagogical review of "interaction distance" [Nat. Commun. 8, 14926 (2017)] -- a systematic method that quantifies the effect interactions can have on the energy spectrum and on the quantum correlations of generic many-body systems. In particular, the interaction distance is a diagnostic tool that identifies the emergent physics of interacting systems. We illustrate this method on the simple example of a one-dimensional Fermi-Hubbard dimer.