从反超对称哈密顿量平方根实现 $\mathcal{PT}$ 类相变
摘要
我们提出一种通用框架，用于在不施加显式平衡-时间（）对称性的前提下实现 类相变。该方法基于将反超对称伴侣哈密顿量平方根构成哈密顿量，常数位移移。这种表述自然导致具有平衡增益与损耗的双体动力学，可包含非互易耦合。 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 -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 -symmetry.
引用
@article{arxiv.2511.12833,
title = {$\mathcal{PT}$-like phase transitions from square roots of supersymmetric Hamiltonians},
author = {Jacob L. Barnett and Ramy El-Ganainy},
journal= {arXiv preprint arXiv:2511.12833},
year = {2025}
}
备注
14 pages, 4 figures