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

• URL: http://arxiv.org/abs/2511.12833v1
• Date: Sun, 16 Nov 2025 23:38:51 GMT
• Title: $\mathcal{PT}$-like phase transitions from square roots of supersymmetric Hamiltonians
• Authors: Jacob L. Barnett, Ramy El-Ganainy,
• Abstract summary: We introduce a general framework for realizing $mathcalPT$-like phase transitions in non-Hermitian systems.<n>This work uncovers new links between non-Hermitian physics and supersymmetry.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a general framework for realizing $\mathcal{PT}$-like phase transitions in non-Hermitian systems without imposing explicit parity--time ($\mathcal{PT}$) 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 $\mathcal{PT}$-symmetry.

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