$\mathcal{PT}$-like phase transitions from square roots of supersymmetric Hamiltonians

Jacob L. Barnett; Ramy El-Ganainy

doi:10.1103/srqj-8n5w

paper

$P T$ -like phase transitions from square roots of supersymmetric Hamiltonians

arXiv:2511.12833 · doi:10.1103/srqj-8n5w

Abstract

We introduce a general framework for realizing $P T$ -like phase transitions in non-Hermitian systems without imposing explicit parity--time ( $P T$ ) symmetry. The approach is based on constructing a Hamiltonian as the square root of a supersymmetric partner energy-shifted by a constant. This formulation naturally leads to bipartite dynamics with balanced gain and loss and can incorporate non-reciprocal couplings. The resulting systems exhibit entirely real spectra over a finite parameter range precisely when the corresponding passive Hamiltonian lacks a zero mode. As the non-Hermitian parameter representing gain and loss increases, the spectrum undergoes controlled real-to-complex transitions at second-order exceptional points. We demonstrate the versatility of this framework through several examples, including well-known models such as the Hatano--Nelson (HN) and complex Su--Schrieffer--Heeger (cSSH) lattices. Extending the formalism to $q$ -commuting matrices further enables the systematic realization of higher-order exceptional points in systems with unidirectional couplings. Overall, this work uncovers new links between non-Hermitian physics and supersymmetry, offering a practical route to engineer photonic arrays with tunable spectral properties beyond what is achievable with explicit $P T$ -symmetry.

14 pages, 4 figures

PT-like phase transitions from square roots of supersymmetric Hamiltonians

Abstract

References in corpus (23)

$P T$ -like phase transitions from square roots of supersymmetric Hamiltonians