Properties of exceptional points in some many body models
The Lipkin model is a popular toy model, first used in nuclear physics, to understand quantum phase transitions including symmetry breaking. However, the thermodynamic limit, that is the limit of large particle numbers, appears rather elusive. The pattern of the exceptional points of the model, in particular their behavior with increasing particle numbers, is presented. They may give a clue as to the properties of the Lipkin Hamiltonian in the thermodynamic limit.
Key wordsphase transitions singularities of spectra non-Hermitian operators
Unable to display preview. Download preview PDF.
- P. Ring and P. Schuck: The Nuclear Many Body Problem, Springer, New York, 1980.Google Scholar
- F.G. Scholtz, B.H. Bartlett, and H.B. Geyer: Phys. Rev. Lett. 91 (2004) 80602. J.N. Kriel, A. Morozov, and F.G. Scholtz: J. Phys. A 38 (2005) 205.Google Scholar
- T. Kato: Perturbation theory of linear operators, Springer, Berlin, 1966.Google Scholar
- W.D. Heiss: Z. Phys. A: Atom. Nucl. 329 (1988) 133.Google Scholar
- P. Cejnar, S. Heinze, and J. Dobes: Preprint nucl-th/0406060.Google Scholar