Abstract
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).
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
