Frustration, interaction strength and ground-state entanglement in complex quantum systems

Details Frustration, interaction strength and ground-state entanglement in complex quantum systems Frustration, interaction strength and ground-state entanglement in complex quantum systems

2004-01-12

arxiv.org/abs/quant-ph/0401061v3

Phys. Rev. A 69 (5): Art. No. 052316 (2004)

Physics

Quantum Physics

11 pages, 3 figures

Scientific paper

10.1103/PhysRevA.69.052316

Entanglement in the ground state of a many-body quantum system may arise when the local terms in the system Hamiltonian fail to commute with the interaction terms in the Hamiltonian. We quantify this phenomenon, demonstrating an analogy between ground-state entanglement and the phenomenon of frustration in spin systems. In particular, we prove that the amount of ground-state entanglement is bounded above by a measure of the extent to which interactions frustrate the local terms in the Hamiltonian. As a corollary, we show that the amount of ground-state entanglement is bounded above by a ratio between parameters characterizing the strength of interactions in the system, and the local energy scale. Finally, we prove a qualitatively similar result for other energy eigenstates of the system.

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