# Particle partition entanglement of one dimensional spinless fermions

## TL;DR

This paper studies how the entanglement entropy of particle partitions in one-dimensional spinless fermions scales with system size, revealing universal behaviors in the Tomonaga-Luttinger liquid regime and confirming results through numerical methods.

## Contribution

It provides a detailed analysis of particle partition entanglement scaling in 1D fermionic systems, highlighting universality and boundary condition effects, supported by exact diagonalization.

## Key findings

- Universal logarithmic scaling of entanglement entropy with system size.
- Higher-order corrections decay as power-laws depending on the Luttinger parameter.
- Particle entanglement is sensitive to boundary conditions and statistics.

## Abstract

We investigate the scaling of the R\'{e}nyi entanglement entropies for a particle bipartition of interacting spinless fermions in one spatial dimension. In the Tomonaga-Luttinger liquid regime, we calculate the second R\'{e}nyi entanglement entropy and show that the leading order finite-size scaling is equal to a universal logarithm of the system size plus a non-universal constant. Higher-order corrections decay as power-laws in the system size with exponents that depend only on the Luttinger parameter. We confirm the universality of our results by investigating the one dimensional $t-V$ model of interacting spinless fermions via exact-diagonalization techniques. The resulting sensitivity of the particle partition entanglement to boundary conditions and statistics supports its utility as a probe of quantum liquids.