Genuine tripartite entanglement as a probe of quantum phase transitions in a spin-1 Heisenberg chain with single-ion anisotropy

TL;DR

This paper investigates how genuine tripartite entanglement can be used to identify quantum phase transitions in a spin-1 Heisenberg chain with anisotropy, revealing clear entanglement signatures at phase boundaries.

Contribution

It introduces a multipartite entanglement measure based on the tripartite qutrit hyperdeterminant to detect phase transitions in spin chains with anisotropy.

Findings

Tripartite entanglement exhibits a plateau in the Haldane phase.

Abrupt drops in entanglement mark phase boundaries.

Entanglement effectively probes topological phases.

Abstract

We study the quantum phase transitions of spin-1 Heisenberg chains with an easy-axis anisotropy $\Delta$ and a uniaxial single-ion anisotropy $D$ using a multipartite entanglement approach. The genuine tripartite entanglement between the spin blocks, measured by the tripartite qutrit hyperdeterminant, is calculated within the quantum renormalization group method. Using this approach, the phase boundaries between the topological Haldane, large-D and anti-ferromagnetic N\'eel phases are determined in the half $\Delta-D$ plane with $\Delta>0$. When the size of the spin blocks increases, the genuine tripartite entanglement between the blocks exhibits a nonzero plateau in the topological Haldane phase, and experiences abrupt drops at both the phase boundaries between the Haldane--large-D and Haldane--N\'eel phases, which justifies the usage of genuine multipartite entanglement as a probe of topological phases in spin systems.