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arXiv · 1103.0022

Characterizing and Quantifying Frustration in Quantum Many-Body Systems

S. M. Giampaolo·G. Gualdi·A. Monras·F. Illuminati
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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.

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S. M. Giampaolo, G. Gualdi, A. Monras, F. Illuminati. 2012-01-05. Characterizing and Quantifying Frustration in Quantum Many-Body Systems. https://doi.org/10.1103/physrevlett.107.260602

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