Entanglement dynamics via geometric phases in quantum spin chains

TL;DR

This paper establishes a link between geometric phases and entanglement in quantum spin chains, showing that the interaction geometric phase can serve as an indicator of global entanglement during evolution.

Contribution

It introduces a novel relationship between interaction geometric phases and global entanglement in spin chains, providing a potential tool for quantum information tasks.

Findings

Interaction geometric phase relates to global entanglement.

Analytical proof for two spins, numerical for larger chains.

Interaction geometric phase can indicate entanglement levels.

Abstract

We introduce a connection between entanglement induced by interaction and geometric phases acquired by a composite quantum spin system. We begin by analyzing the evaluation of cyclic (Aharonov-Anandan) and non-cyclic (Mukunda-Simon) geometric phases for general spin chains evolving in the presence of time-independent magnetic fields. Then, by considering Heisenberg chains, we show that the interaction geometric phase, namely, the total geometric phase with subtraction of free spin contributions, is directly related to the global (Meyer-Wallach) entanglement exhibited by an initially separable state during its evolution in Hilbert space. This is analytically shown for N=2 spins and numerically illustrated for larger chains. This relationship promotes the interaction geometric phase to an indicator of global entanglement in the system, which may constitute a useful tool for quantum tasks based on entanglement as a resource to their performance.