Characterizing and quantifying frustration in quantum many-body systems
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 th...
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| Published in | Physical review letters Vol. 107; no. 26; p. 260602 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
United States
23.12.2011
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| Online Access | Get more information |
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| Summary: | 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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| ISSN: | 1079-7114 |
| DOI: | 10.1103/PhysRevLett.107.260602 |