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.
@article{arxiv.1103.0022,
title = {Characterizing and Quantifying Frustration in Quantum Many-Body Systems},
author = {S. M. Giampaolo and G. Gualdi and A. Monras and F. Illuminati},
journal= {arXiv preprint arXiv:1103.0022},
year = {2012}
}