title: Characterizing and quantifying frustration in quantum many-body systems.
abstract: We present a general scheme for the study of frustration in quantum systems. We introduce a universal measure of frustration for arbitrary quantum systems and we relate it to a class of entanglement monotones via an exact inequality. If all the (pure) ground states of a given Hamiltonian saturate the inequality, then the system is said to be inequality saturating. We introduce sufficient conditions for a quantum spin system to be inequality saturating and confirm them with extensive numerical tests. These conditions provide a generalization to the quantum domain of the Toulouse criteria for classical frustration-free systems. The models satisfying these conditions can be reasonably identified as geometrically unfrustrated and subject to frustration of purely quantum origin. Our results therefore establish a unified framework for studying the intertwining of geometric and quantum contributions to frustration.
authors.affiliation: Dipartimento di Ingegneria Industriale, Università degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA), Italy.
authors.forename: S M
authors.initials: SM
authors.lastname: Giampaolo
authors.forename: G
authors.initials: G
authors.lastname: Gualdi
authors.forename: A
authors.initials: A
authors.lastname: Monras
authors.forename: F
authors.initials: F
authors.lastname: Illuminati