Entanglement in fermionic systems

TL;DR

This paper explores how fermionic properties and parity conservation influence the concept of entanglement, providing a detailed classification of separable states in two-fermion systems and analyzing their implications for quantum states like Gibbs states.

Contribution

It offers a comprehensive analysis of different definitions of entanglement in fermionic systems and characterizes separable states for two-fermion modes, linking theory to physical models.

Findings

Complete characterization of separable states for two fermionic modes

Different definitions of entanglement lead to distinct state classifications

Application to Gibbs states of fermionic chains with XY-Hamiltonian

Abstract

The anticommuting properties of fermionic operators, together with the presence of parity conservation, affect the concept of entanglement in a composite fermionic system. Hence different points of view can give rise to different reasonable definitions of separable and entangled states. Here we analyze these possibilities and the relationship between the different classes of separable states. We illustrate the differences by providing a complete characterization of all the sets defined for systems of two fermionic modes. The results are applied to Gibbs states of infinite chains of fermions whose interaction corresponds to a XY-Hamiltonian with transverse magnetic field.