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Zeitschrift für Naturforschung A Contents Vol. 67a (2012)

Z. Naturforsch. 67a, 608 – 612 (2012)

doi:10.5560/ZNA.2012-0064

Spin Hamilton Operators, Symmetry Breaking, Energy Level Crossing, and Entanglement

Willi-Hans Steeb¹, Yorick Hardy², and Jacqueline de Greef¹

¹International School for Scientific Computing, University of Johannesburg, Auckland Park 2006, South Africa

²Department of Mathematical Sciences, University of South Africa, Pretoria, South Africa

Received June 12, 2012 / published online August 20, 2012

Reprint requests to: W.-H. S.; E-mail: steebwilli@gmail.com

We study finite-dimensional product Hilbert spaces, coupled spin systems, entanglement, and energy level crossing. The Hamilton operators are based on the Pauli group. We show that swapping the interacting term can lead from unentangled eigenstates to entangled eigenstates and from an energy spectrum with energy level crossing to avoided energy level crossing.

Key words: Hilbert Space; Energy Level Crossing; Discrete Symmetries; Entanglement.

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