Pairwise Entanglement and Geometric Phase in $d=2,3$-Dimensional Free-Fermion Lattice Systems

TL;DR

This paper investigates how pairwise entanglement and geometric phase in 2D and 3D free-fermion lattice systems can signal phase transitions and relate to correlation functions, providing insights into quantum critical phenomena.

Contribution

It introduces a method to detect phase transitions via derivatives of entanglement and geometric phase, and explores their connection to correlation functions in free-fermion models.

Findings

Concurrence and geometric phase exhibit singularities near phase transition points.

Both measures are closely related to correlation functions in the system.

The study discusses potential links between concurrence and geometric phase.

Abstract

The pairwise entanglement, measured by concurrence and geometric phase in $d=2,3$-dimensional free-fermion lattice systems have been studied for the ground state in this paper. Their derivation with respect to the external parameter show the singularity closed to the phase transition points, and can be used to detect the phase transition in this model. Furthermore our studies show for the free-fermion model that both concurrence and geometric phase shows the intimate connection with the correlation functions. The possible relation between concurrence and geometric phase has been also discussed.