Hidden antiunitary symmetry behind "accidental" degeneracy and its protection of degeneracy

TL;DR

This paper reveals that what appears as accidental degeneracy in quantum systems is actually protected by a hidden antiunitary symmetry, providing a new perspective on degeneracy protection.

Contribution

It proves a theorem showing all two-fold degeneracies are protected by a hidden antiunitary symmetry, redefining the understanding of accidental degeneracy in quantum mechanics.

Findings

Two-fold degeneracies are protected by a hidden antiunitary symmetry.

Accidental degeneracy is not truly accidental but symmetry-protected.

The hidden symmetry is represented by an antiunitary operator with square -1.

Abstract

In quantum mechanics, accidental degeneracy refers to energy degeneracy that occurs coincidentally, without any protection by symmetry. Here, we prove a theorem stating that any two-fold degeneracy (accidental or not) in a quantum system is protected by a novel hidden symmetry, which can be expressed by an antiunitary operator with its square being -1. In this sense, the so-called accidental degeneracy is not really accidental, and this actually implies a hidden antiunitary symmetry.