# Evolution from few- to many-body physics in one-dimensional Fermi systems: One- and two-body density matrices, and particle-partition entanglement

## TL;DR

This paper investigates the transition from few- to many-body physics in one-dimensional attractive Fermi systems, analyzing density matrices, momentum distribution, and entanglement to understand their evolving quantum properties.

## Contribution

It provides detailed analysis of one- and two-body density matrices, momentum distribution, and entanglement in 1D fermionic systems, extending understanding from few- to many-body regimes.

## Key findings

- Momentum distribution scaling yields sound speed and Tan's contact consistent with prior work.
- One-body density matrices show characteristic features of many-body systems.
- Particle-partition entanglement entropy scales logarithmically with particle number.

## Abstract

We study the evolution from few- to many-body physics of fermionic systems in one spatial dimension with attractive pairwise interactions. We determine the detailed form of the momentum distribution, the structure of the one-body density matrix, and the pairing properties encoded in the two-body density matrix. From the low- and high-momentum scaling behavior of the single-particle momentum distribution we estimate the speed of sound and Tan's contact, respectively. Both quantities are found to be in agreement with previous calculations. Based on our calculations of the one-body density matrices, we also present results for the particle-partition entanglement entropy, for which we find a logarithmic dependence on the total particle number.