Confluences of exceptional points and a systematic classification of quantum catastrophes

TL;DR

This paper explores quantum phase transitions linked to exceptional points, classifying quantum catastrophes based on mathematical properties of these points, and illustrates mechanisms of such transitions with solvable models.

Contribution

It introduces a systematic classification of quantum catastrophes based on algebraic and geometric multiplicities of exceptional points, supported by solvable toy models.

Findings

Classifies quantum catastrophes using algebraic and geometric multiplicities.

Demonstrates mechanisms of EP-merger transitions with solvable models.

Provides insights into the mathematical structure of quantum phase transitions.

Abstract

Specific quantum phase transitions of our interest are assumed associated with the fall of a closed, unitary quantum system into its exceptional-point (EP) singularity. The physical realization of such a "quantum catastrophe" (connected, typically, with an instantaneous loss of the diagonalizability of the corresponding parameter-dependent Hamiltonian $H(g)$) depends, naturally, on the formal mathematical characteristics of the EP, i.e., in essence, on its so called algebraic multiplicity $N$ and geometric multiplicity $K$. In our paper we assume that both of them are finite, and we illustrate and discuss, using several solvable toy models, some of the most elementary mechanisms of the EP-merger realization of the process of the transition $g \to g^{(EP)}$.