Phase diagram and scaling behavior of a PT symmetric non-Hermitian Bose-Hubbard system

Details Phase diagram and scaling behavior of a PT symmetric non-Hermitian Bose-Hubbard system Phase diagram and scaling behavior of a PT symmetric non-Hermitian Bose-Hubbard system

2011-05-31

arxiv.org/abs/1105.6186v2

Physics

Condensed Matter

Statistical Mechanics

9 pages, 3 figures

Scientific paper

We study scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard model. In the free interaction case, using both analytical and numerical approaches, the metric operator for many-particle is constructed. The derived properties of the metric operator, similarity matrix and equivalent Hamiltonian reflect the fact that all the matrix elements change dramatically with diverging derivatives near the exceptional point. In the nonzero interaction case, it is found that even small on-site interaction can break the PT symmetry drastically. It is demonstrated that the scaling law can be established for the exceptional point in small interaction limit. Based on numerical approach, we also find that the phase diagram shows rich structure in the medium interaction case: there exist multiple regions of unbroken PT symmetry.

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