Generalized Bose-Hubbard Hamiltonians exhibiting a complete non-Hermitian degeneracy

0505684 - ÚJF 2020 RIV US eng J - Journal Article
Znojil, Miloslav
Generalized Bose-Hubbard Hamiltonians exhibiting a complete non-Hermitian degeneracy.
Annals of Physics. Roč. 405, č. 6 (2019), s. 325-339. ISSN 0003-4916. E-ISSN 1096-035X
R&D Projects: GA ČR GA16-22945S
Institutional support: RVO:61389005
Keywords : non-Hermitian quantum dynamics * multilevel degeneracies * higher-order exceptional points
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 2.083, year: 2019
Method of publishing: Limited access
https://doi.org/10.1016/j.aop.2019.03.022

The method of construction of the tridiagonal and symmetric complex-matrix Hamiltonians H-(N)(z) exhibiting an exceptional point (EP) degeneracy of the Nth (i.e., maximal) order at a preselected parameter z = z((EPN)) = 1 is proposed and tested. In general, the implementation of the method requires the use of computer-assisted symbolic manipulations, especially at the larger matrix dimensions N. The well known PT-symmetric N-by-N-matrix Bose-Hubbard Hamiltonians as well as their recent N <= 5 non-Bose-Hubbard alternatives are obtained as special solutions. Several other N >= 6 non-Bose-Hubbard models H-(N)(z) exhibiting the maximal EPN degeneracy are also constructed and analyzed in detail. In particular, their z-dependent, real or complex spectra of energies are displayed and discussed near as well as far from z((EPN)).
Permanent Link: http://hdl.handle.net/11104/0297096