Dynamical symmetry in a minimal dimeric complex

TL;DR

This paper investigates a minimal dimeric hexagonal complex, revealing an internal $U(3)$ symmetry at a degeneracy point and exploring its implications for hidden symmetries in quantum systems.

Contribution

It identifies a dynamical $U(3)$ symmetry in a minimal dimeric system and analyzes its manifestation in phase space and implications for hidden symmetries.

Findings

Accidental three-fold degeneracy point discovered

Internal $U(3)$ symmetry operates on Hilbert space

Invariant subset shown in a 6x6 phase space

Abstract

The emergence of non-configurational symmetry is studied in a minimal example. The system under scrutiny consists of a dimeric hexagonal complex with configurational $C_3$ symmetry, formulated as a tight-binding model. An accidental three-fold degeneracy point in parameter space is found; it is shown that an internal $U(3)$ symmetry group operates on Hilbert space, but not on configuration space. The corresponding discrete Wigner functions for the irreducible representations of $C_6 \cong C_3 \times Z_2$ are utilized to show that a $6\times 6$ phase space is sufficient to exhibit an invariant subset. The dynamical symmetry is thus identified with a discrete semi-plane. Some implications on other known hidden symmetries of continuous systems are qualitatively discussed.