Multiply Degenerate Exceptional Points and Quantum Phase Transitions

TL;DR

This paper introduces a new family of finite-dimensional quantum lattice models that exhibit exceptional points at real times, modeling quantum phase transitions and simulating Big-Bang-like quantum catastrophes.

Contribution

It proposes and analyzes a novel class of time-dependent quantum models with real exceptional points, linking spectral degeneracies to quantum phase transitions.

Findings

Models exhibit Jordan-block degeneracy at real exceptional points

Passages through critical times simulate quantum catastrophes

Spectral properties relate to phase transition dynamics

Abstract

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.