2011/03/31 by S. M. Giampaolo, G. Gualdi, A. Monras +1 · 1 citation
Physics and Astronomy · Mathematics · #cond-mat.other #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physrevlett.107.260602
published as Phys. Rev. Lett. 107, 260602 (2011) · 8 pages, 1 figure
arxiv created 2012/01/05 · arxiv updated 2012/01/06
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.