Characterizing and Quantifying Frustration in Quantum Many-Body Systems

Details Characterizing and Quantifying Frustration in Quantum Many-Body Systems Characterizing and Quantifying Frustration in Quantum Many-Body Systems

2011-02-28

arxiv.org/abs/1103.0022v2

Phys. Rev. Lett. 107, 260602 (2011)

Physics

Condensed Matter

Other Condensed Matter

8 pages, 1 figure

Scientific paper

10.1103/PhysRevLett.107.260602

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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