Entanglement of finite cyclic chains at factorizing fields

TL;DR

This paper investigates how entanglement behaves in finite cyclic spin chains at specific magnetic fields where the ground state becomes separable, revealing universal properties and transitions related to magnetization jumps.

Contribution

It demonstrates that pairwise entanglement remains non-zero at factorizing fields in finite chains, showing universal behavior independent of interaction range and separation.

Findings

Pairwise entanglement limits are non-zero at factorizing fields.

Entanglement limits are independent of pair separation and interaction range.

Ground state exhibits a spin-parity transition at these fields.

Abstract

We examine the entanglement of cyclic spin 1/2 chains with anisotropic XY Z Heisenberg couplings of arbitrary range at transverse factorizing magnetic fields. At these fields the system exhibits a degenerate symmetry-breaking separable ground state (GS). It is shown, however, that the side limits of the GS pairwise entanglement at these fields are actually non-zero in finite chains, corresponding such fields to a GS spin-parity transition. These limits exhibit universal properties like being independent of the pair separation and interaction range, and are directly related to the magnetization jump. Illustrative exact results are shown for chains with I) full range and II) nearest neighbor couplings. Global entanglement properties at such points are also discussed.