Ground state factorization versus frustration in spin systems

 

We investigate the existence of factorized ground states in Heisenberg-like quantum spin models with antiferromagnetic interactions  of arbitrary range and exhibiting a varying degree of frustration. After reviewing a method developed for frustration-free systems based on tools from quantum information theory, we extend it to characterize the competition between frustration and ground state factorization. Low frustration is shown to signaled by the existence of factorized ground states at specific values of the external field, while for higher  frustration degrees the factorized eigenstates do not minimize the energy, leaving necessarily room for entanglement in the ground state. The compatibility threshold, characterizing the frustration-driven transition between order (factorization) and disorder (correlation), is investigated and exact analytical factorized solutions are obtained for short-range as well as infinite-range frustrated quantum magnets.Ground state factorization is thus revealed as an effective tool to probe quantum frustration in cooperative systems.