-like phase transitions from square roots of supersymmetric Hamiltonians
Phys. Rev. A 114, 013507 – Published 7 July, 2026
DOI: https://doi.org/10.1103/srqj-8n5w
Abstract
We introduce a general framework for realizing parity-time -like phase transitions in non-Hermitian systems without imposing explicit 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 nonreciprocal 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 and complex Su-Schrieffer-Heeger lattices. Extending the formalism to -commuting matrices further enables the systematic realization of higher-order exceptional points in systems with unidirectional couplings. Overall, this work uncovers 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 symmetry.
