Ground state factorization of heterogeneous spin models in magnetic fields

TL;DR

This paper derives conditions for the exact factorized ground state in heterogeneous spin models with complex magnetic interactions and fields, expanding understanding of quantum correlations in practical magnetic materials.

Contribution

It provides a detailed analysis of ground state factorization conditions for non-translational invariant heterogeneous spin models under various magnetic fields, including new classifications based on lattice structure.

Findings

Identified conditions for ground state factorization in non-uniform magnetic fields.

Categorized spin models into two classes based on lattice structure and magnetic field effects.

Demonstrated that some models can have a factorized ground state with either uniform or staggered fields.

Abstract

The exact factorized ground state of a heterogeneous (ferrimagnetic) spin model which is composed of two spins ($\rho, \sigma$) has been presented in detail. The Hamiltonian is not necessarily translational invariant and the exchange couplings can be competing antiferromagnetic and ferromagnetic arbitrarily between different sub-lattices to build many practical models such as dimerized and tetramerized materials and ladder compounds. The condition to get a factorized ground state is investigated for non-frustrated spin models in the presence of a uniform and a staggered magnetic field. According to the lattice model structure we have categorized the spin models in two different classes and obtained their factorization conditions. The first class contains models in which their lattice structures do not provide a single uniform magnetic field to suppress the quantum correlations. Some of these models may have a factorized ground state in the presence of a uniform and a staggered magnetic field. However, in the second class there are several spin models in which their ground state could be factorized whether a staggered field is applied to the system or not. For the latter case, in the absence of a staggered field the factorizing uniform field is unique. However, the degrees of freedom for obtaining the factorization conditions are increased by adding a staggered magnetic field.