Separability and entanglement in finite dimer-type chains in general transverse fields

TL;DR

This paper explores the conditions for exact separability and entanglement properties in finite dimer-type spin chains with XYZ couplings under various transverse fields, revealing how entanglement ranges and ground states are affected.

Contribution

It provides new criteria for exact separability and entanglement behavior in finite dimer chains with arbitrary interactions and fields, including non-uniform cases.

Findings

Exact conditions for separable eigenstates are derived.

Entanglement becomes infinite-range near separability.

Non-uniform fields can induce separable ground states.

Abstract

We determine the conditions under which general dimer-type spin chains with $XYZ$ couplings of arbitrary range in a general transverse field will exhibit an exactly separable parity-breaking eigenstate. We also provide sufficient conditions which ensure that it will be a ground state. We then examine the exact side limits at separability of the entanglement between any two spins in a finite chain, showing that in the vicinity of separability, the system will loose all signatures of dimerization, with pairwise entanglement approaching infinite range and becoming independent of separation and interaction range. The possibility of a non-uniform exactly separable ground state induced by an alternating field is also shown. As illustration, we examine the behavior of the pairwise entanglement in a finite $XY$ dimer chain under a uniform as well as alternating field. Related aspects of the magnetization are also discussed.