Non-Abelian Gauge Enhances Self-Healing for Non-Hermitian Su--Schrieffer--Heeger Chain

TL;DR

This work introduces a non-Hermitian SSH chain enriched by spin-dependent SU(2) gauge fields, yielding spin-selective hopping and a rich phase structure marked by complex-energy braiding and gauge-tunable NHSE. Using the generalized Brillouin zone, it establishes a consistent bulk-boundary correspondence and identifies chiral-symmetry-protected topological transitions. A central result is that non-Abelian gauge fields substantially enhance dynamical self-healing of skin-localized modes under time-dependent perturbations, providing a robust mechanism for stabilizing edge-state transport. The findings map out phase diagrams and GBZ geometries and are relevant to photonic, magnonic, cold-atom, and superconducting platforms, where SU(2) gauge control can be used to tailor non-Hermitian topology and robustness.

Abstract

We investigate a non-Hermitian extension of the Su--Schrieffer--Heeger model that incorporates spin-dependent SU(2) gauge fields, represented by non-Abelian couplings between lattice sites, as well as independent nonreciprocal hopping amplitudes. This framework gives rise to a rich phase structure characterized by complex-energy braiding and tunable non-Hermitian skin effects. By employing the generalized Brillouin zone approach, we analyze the bulk-boundary correspondence and identify topological transitions protected by chiral symmetry. Notably, we demonstrate that non-Abelian gauge fields significantly enhance the dynamical resilience of the system, enabling robust self-healing under a moving scattering potential. These results clarify the role of SU(2) gauge fields in stabilizing non-Hermitian topological phases and indicate that the proposed model can be realized with currently available photonic, atomic, and superconducting experimental platforms.

Figures (8)

• Figure 1: Schematic of the non-Hermitian non-Abelian SU(2) SSH model. Each unit cell (dotted box) contains two sublattice sites, labeled $A$ and $B$, and each site hosts a spin-$1/2$ degree of freedom. The hopping amplitudes $t_1, t_2, t_3, t_4$ connect sublattices within (and across) unit cells, while the SU(2) rotation matrices $U_L$ and $U_R$ endow these processes with spin-dependent phases.
• Figure 2: Phase diagrams, braiding and complex-energy spectrum. (a) Phase diagram versus $\theta_{L}$ and $\theta_{R}$ at $(t_1,t_2,t_3,t_4)=(0.60,1.00,0.80,0.89)$. Points $(\theta_L,\theta_R)=(-2.6,0.6)$, $(-0.874,0.6)$, and $(1.4,0.6)$ correspond to (b), (c), and (d). (b)--(d) Braiding and complex-energy spectra under periodic (color loops) and open boundary conditions (black arcs). In (c), the closed loops in $(\mathrm{Re}\,E,\mathrm{Im}\,E,k)$, as well as their projection onto the complex-energy plane are actually formed by two different bands (EP-mediated). $N=49$ hereafter for calculations about real space Hamiltonians. The legend of (c) and (d) is identical to that of (b).
• Figure 3: GBZ and distribution of eigenstates. (a), (c), (e) GBZ trajectories corresponding to the parameters indicated by solid circle, square and triangle indicated in FIG. \ref{['figphaseEnergy']} (a), respectively. The points located inside the unit circle are colored blue, those located outside the unit circle are colored red, while the black points construct the unit circle. (b), (d), (f) Spatial distributions of the eigenstates under OBC at the corresponding parameters. The gray curves are used to visually represent the color mapping of the eigenstate-population probability.
• Figure 4: Comparison between the representative self-healing case (blue) and the no self-healing case (red) under the same scattering potential. The curves show the deviation metric $\varepsilon(t)$. Insets correspond to wavefunction intensity $|\psi_j|^2$ sampled at the arrow-indicated times, before and after the scattering interval. For the self-healing state, the post-scattering profile recovers and remains the same as the initial one (SAME), whereas the no self-healing state fails to restore its original profile (DIFFERENT).
• Figure 5: Wavefunction evolution from two different OBC eigenstates with the largest $\mathrm{Im}\,(E)$: (a) with non-Abelian coupling and (b) without it. Both cases use $t_1=0.60$, $t_2=1.00$, $t_3=0.80$, $t_4=0.89$, with gauge phases (a) $\theta_L=1.4,\;\theta_R=0.6$ and (b) $\theta_L=\theta_R=0$. Panels 1--4 on the right are zoom-ins of the left panels: 1 and 2 from (a) and 3 together with 4 from (b); each pair shows the unperturbed initial state and the post-scattering state. The amber dashed line marks the trajectory of the moving scattering potential.