Factorization in XYZ spin systems under general fields and separable ground state engineering

TL;DR

This paper explores how to engineer exactly separable ground states in XYZ spin systems with arbitrary couplings and fields, demonstrating the feasibility of tuning parameters to achieve and control factorization and entanglement.

Contribution

It provides a general framework for creating and tuning separable ground states in complex XYZ spin systems with non-uniform couplings and fields.

Findings

Existence of exactly separable eigenstates with arbitrary spin orientations.

Feasibility of tuning fields to reach nondegenerate ground states.

Near factorization, pairwise entanglement becomes long-range.

Abstract

We discuss ground state factorization schemes in spin $S$ arrays with general $XYZ$ couplings under general magnetic fields, not necessarily uniform or transverse. It is first shown that given arbitrary spin alignment directions at each site, nonzero couplings between any pair and fields at each site always exist such that the ensuing Hamiltonian has an exactly separable eigenstate with the spins pointing along the specified directions. Furthermore, by suitable tuning of the fields this eigenstate can always be cooled down to a nondegenerate ground state. It is also shown that in open one-dimensional systems with arbitrary $XYZ$ first neighbor couplings, at least one separable eigenstate compatible with an arbitrarily chosen spin direction at one site is always feasible if the fields at each site can be tuned. We demonstrate as well that in the vicinity of factorization, i.e., for small perturbations in the fields or couplings, pairwise entanglement reaches full range. Some noticeable examples of factorized eigenstates for uniform couplings are unveiled. The present results open the way for separable ground state engineering. A notation to quantify the complexity of a given type of solution according to the required control on the system couplings and fields is introduced.