Factorization and criticality in finite XXZ systems of arbitrary spin

TL;DR

This paper investigates ground state factorization in finite XXZ spin systems of arbitrary spin, revealing conditions for separable states, their critical properties, and the effects of various field configurations on entanglement and frustration.

Contribution

It provides a comprehensive analysis of ground state factorization in XXZ systems with arbitrary spins and nonuniform fields, including analytical determination of factorized states and their critical entanglement properties.

Findings

Degenerate separable ground states can occur at quantum critical points.

Factorized states depend only on exchange anisotropies.

Certain field configurations induce frustration and complex behavior.

Abstract

We analyze ground state (GS) factorization in general arrays of spins $s_i$ with $XXZ$ couplings immersed in nonuniform fields. It is shown that an exceptionally degenerate set of completely separable symmetry-breaking GS's can arise for a wide range of field configurations, at a quantum critical point where all GS magnetization plateaus merge. Such configurations include alternating fields as well as zero bulk field solutions with edge fields only and intermediate solutions with zero field at specific sites, valid for $d$-dimensional arrays. The definite magnetization projected GS's at factorization can be analytically determined and depend only on the exchange anisotropies, exhibiting critical entanglement properties. We also show that some factorization compatible field configurations may result in field-induced frustration and nontrivial behavior at strong fields.