# Operationally accessible entanglement of one dimensional spinless fermions

## TL;DR

This paper investigates the accessible entanglement in one-dimensional spinless fermions, revealing how it varies across phase transitions and relates to particle number fluctuations, using exact numerical methods.

## Contribution

It quantifies the operationally accessible entanglement in a 1D fermionic model and links it to phase transitions and particle fluctuations, providing new insights into quantum resources.

## Key findings

- Accessible entanglement vanishes at the transition between Tomonaga-Luttinger liquid and phase separated solid.
- Accessible entanglement is maximal at the transition to charge density wave for repulsive interactions.
- Accessible entanglement correlates with particle number fluctuation variance across the phase diagram.

## Abstract

For indistinguishable itinerant particles subject to a superselection rule fixing their total number, a portion of the entanglement entropy under a spatial bipartition of the ground state is due to particle fluctuations between subsystems and thus is inaccessible as a resource for quantum information processing. We quantify the remaining operationally accessible entanglement in a model of interacting spinless fermions on a one dimensional lattice via exact diagonalization and the density matrix renormalization group. We find that the accessible entanglement exactly vanishes at the first order phase transition between a Tomonaga-Luttinger liquid and phase separated solid for attractive interactions and is maximal at the transition to the charge density wave for repulsive interactions. Throughout the phase diagram, we discuss the connection between the accessible entanglement entropy and the variance of the probability distribution describing intra-subregion particle number fluctuations.