Ground-state factorization and quantum phase transition in dimerized spin chains

TL;DR

This paper investigates ground-state factorization in dimerized XY spin chains, revealing unique degeneracy points and extending the analysis to broader models, thus advancing understanding of quantum phase transitions in complex spin systems.

Contribution

It provides the exact solution for dimerized XY chains and identifies conditions for ground-state factorization, including a novel degeneracy point absent in translationally-invariant systems.

Findings

Identification of a third regime with Neél-type ground state

Exact solution of the dimerized XY model

Ground-state factorization occurs at an accidental degeneracy point

Abstract

We study the occurrence of ground-state factorization in dimerized $XY$ spin chains in a transverse field. Together with the usual ferromagnetic and antiferromagnetic regimes, a third case emerges, with no analogous in translationally-invariant systems, consisting of an antiferromagnetic Ne\'{e}l-type ground state where pairs of spins represent the unitary cell. Then, we calculate the exact solution of the model and show that the factorizing field represent an accidental degeneracy point of the Hamiltonian. Finally, we extend the study of the existence of ground-state factorization to a more general class of models.