耦合费米子的非厄米 $sl(2)$ 仿射 Toda 模型中的双正交 Majorana 零模、ELC 波与孤子–费米子对偶性
Biorthogonal Majorana zero modes, ELC waves and soliton-fermion duality in non-Hermitian $sl(2)$ affine Toda coupled to fermions
AI总结：
本文研究耦合费米子的非厄米 $sl(2)$ 仿射 Toda 模型，揭示孤子–费米子对偶及钉扎于例外点的双正交 Majorana 零模。
摘要：
我们通过孤子理论技术以及伪手征和伪厄米对称性的实现，研究了一个耦合费米子的非厄米（NH）$sl(2)$ 仿射 Toda 模型。非厄米性、可积性、非线性与拓扑之间的相互作用，显著影响连续束缚态模（CBM）和局域连续谱中的扩展波（ELC）的形成与行为。文中揭示了非厄米孤子–费米子对偶性、复标量场拓扑荷以及谱拓扑中的绕数。双正交 Majorana 零模与具有拓扑荷 $\frac{2}{\pi}\arg{(z=\pm i)}=\pm 1$ 的 NH Toda 孤子对偶，出现在复能量点隙处并被钉扎在零能。零本征值 $ł(z=\pm i)=0$ 除作为零模外，还扮演例外点（EP）的角色；对于反线性对称性 $\mathcal{A}\in\{\mathcal{P}\mathcal{T},\gamma_5\mathcal{P}\mathcal{T}\}$，每个 EP 分隔实本征值的 $\mathcal{A}$ 对称区与 $\mathcal{A}$ 对称性破缺区。我们的发现增进了对奇异量子态的理解，也为未来利用非厄米现象开展拓扑量子计算研究，以及在物质拓扑相理论中探索可积性和 NH 孤子铺平了道路。
英文摘要：
We study a non-Hermitian (NH) $sl(2)$ affine Toda model coupled to fermions through soliton theory techniques and the realizations of the pseudo-chiral and pseudo-Hermitian symmetries. The interplay of non-Hermiticity, integrability, nonlinearity, and topology significantly influence the formation and behavior of a continuum of bound state modes (CBM) and extended waves in the localized continuum (ELC). The non-Hermitian soliton-fermion duality, the complex scalar field topological charges and winding numbers in the spectral topology are uncovered. The biorthogonal Majorana zero modes, dual to the NH Toda solitons with topological charges $\frac{2}π \arg{(z=\pm i)}=\pm 1$, appear at the complex-energy point gap and are pinned at zero energy. The zero eigenvalue $ł(z = \pm i)=0$, besides being a zero mode, plays the role of exceptional points (EPs), and each EP separates a real eigenvalue ${\cal A}$-symmetric and ${\cal A}$-symmetry broken regimes for an antilinear symmetry ${\cal A}\in \{ {\cal P}{\cal T}, \g_5{\cal P}{\cal T}\}$. Our findings improve the understanding of exotic quantum states, but also paves the way for future research in harnessing non-Hermitian phenomena for topological quantum computation, as well as the exploration of integrability and NH solitons in the theory of topological phases of matter.
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