Quantum Information Processing

, Volume 13, Issue 2, pp 299–308 | Cite as

An eigenvalue problem for a Fermi system and Lie algebras

Article

Abstract

We study a Fermi Hamilton operator \(\hat{K}\) which does not commute with the number operator \(\hat{N}\). The eigenvalue problem and the Schrödinger equation are solved. Entanglement is also discussed. Furthermore, the Lie algebra generated by the two terms of the Hamilton operator is derived, and the Lie algebra generated by the Hamilton operator and the number operator is also classified.

Keywords

Fermi operators Entanglement Eigenvalue problem   Majorana Fermions on the lattice 

Notes

Acknowledgments

The authors are supported by the National Research Foundation (NRF), South Africa. This work is based upon research supported by the National Research Foundation. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the author(s), and therefore, the NRF do not accept any liability in regard thereto.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.International School for Scientific ComputingUniversity of JohannesburgJohannesburgSouth Africa
  2. 2.Department of Mathematical SciencesUniversity of South AfricaPretoriaSouth Africa

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