The Horizons of Observability in PT-symmetric Four-site Quantum Lattices

Abstract

One of the key merits of PT-symmetric (i.e., parity times time reversal symmetric) quantum Hamiltonians H lies in the existence of a horizon of the stability of the system. Mathematically speaking, this horizon is formed by the boundary of the domain D^(H) ⊂ R^D of the (real) coupling strengths for which the spectrum of energies is real and non-degenerate, i.e., in principle, observable. It is shown here that even in the elementary circular four-site quantum lattices with D = 2 or D = 3 the domain of hidden Hermiticity D^(H) proves multiply connected, i.e., topologically nontrivial.