Multiply Degenerate Exceptional Points and Quantum Phase Transitions

The realization of a genuine phase transition in quantum mechanics requires that at least one of the Kato’s exceptional-point parameters becomes real. A new family of finite-dimensional and time-parametrized quantum-lattice models with such a property is proposed and studied. All of them exhibit, at a real exceptional-point time t = 0, the Jordan-block spectral degeneracy structure of some of their observables sampled by Hamiltonian H(t) and site-position Q(t). The passes through the critical instant t = 0 are interpreted as schematic simulations of non-equivalent versions of the Big-Bang-like quantum catastrophes.