Unifying Geometric Entanglement and Geometric Phase in a Quantum Phase Transition

TL;DR

This paper unifies geometric entanglement and geometric phase into a complex-valued measure, revealing their singular behavior at quantum critical points and providing a new perspective on quantum phase transitions.

Contribution

It introduces a complex-valued geometric entanglement that combines entanglement and phase, linking them through quantum interferometry and analyzing their critical behavior.

Findings

Complex geometric entanglement captures quantum phase transition signatures.

Singularities occur at critical points due to level crossings.

Unified approach applies to typical quantum systems.

Abstract

Geometric measure of entanglement and geometric phase have recently been used to analyze quantum phase transition in the XY spin chain. We unify these two approaches by showing that the geometric entanglement and the geometric phase are respectively the real and imaginary parts of a complex-valued geometric entanglement, which can be investigated in typical quantum interferometry experiments. We argue that the singular behavior of the complex-value geometric entanglement at a quantum critical point is a characteristic of any quantum phase transition, by showing that the underlying mechanism is the occurrence of level crossings associated with the underlying Hamiltonian.