Latent symmetry in a minimal non-Hermitian trimer

TL;DR

This paper analyzes a minimal non-Hermitian trimer with latent symmetry, revealing exact sector decomposition, $ ext{PT}$-symmetry, and exceptional points, providing a solvable model for complex spectral phenomena.

Contribution

It introduces an exactly solvable non-Hermitian trimer model exhibiting latent symmetry, sector-resolved $ ext{PT}$ symmetry, and embedded exceptional points, advancing understanding of non-Hermitian physics.

Findings

Dark mode is spectrally isolated with a complex eigenvalue.

Bright sector can be $ ext{PT}$-symmetric with real eigenvalues.

Embedded exceptional point causes Jordan-block dynamics.

Abstract

We study a minimal non-Hermitian trimer with latent symmetry formed by a cospectral pair of sites embedded in a three-site network with nonreciprocal couplings. We show that the model admits an exact decomposition into dark and bright sectors: the dark mode is spectrally isolated and retains a complex eigenvalue, while the bright sector reduces to an effective non-Hermitian dimer. For a suitable choice of parameters, this reduced subsystem becomes $\mathcal{PT}$-symmetric and exhibits partial spectral reality, with two real eigenvalues coexisting with the complex dark eigenvalue. At the critical point, the bright sector hosts an embedded second-order exceptional point, which renders the full trimer defective and gives rise to the characteristic Jordan-block dynamics. These results establish the non-Hermitian trimer as a minimal analytically solvable setting in which latent symmetry, sector-resolved $\mathcal{PT}$ symmetry, and exceptional-point physics naturally coexist.