Missing States, Hidden Instabilities: A New View of Non-Hermitian Physics
![The non-Hermitian Su-Schrieffer-Heeger (SSH) model exhibits a complex relationship between system parameters and the presence of zero-energy modes, where, despite the absence of topological edge states in the eigenvalue spectrum-particularly for [latex]1.2 \lesssim |t_1| \leq 5/3[/latex] or [latex]|t_1| \leq 1/3[/latex]-the singular value spectrum consistently identifies these modes, demonstrating its superior capability in detecting zero-energy states compared to solely relying on eigenvalue analysis, even when the system lacks conventional topological protection.](https://arxiv.org/html/2601.05234v1/Figures/NHSSHchain.png)
A new study reveals that discrepancies in non-Hermitian systems stem from focusing on eigenvalues rather than the full eigenstate spectrum, uncovering previously overlooked instabilities.


![Despite an overall appearance of saturation within the many-body localized regime, detailed analysis of site-resolved spin autocorrelators-calculated via unitary time evolution governed by [latex]\text{Eq. (5)}[/latex] and averaged over time as defined in [latex]\text{Eq. (7)}[/latex]-reveals localized resonant dynamics at individual sites, highlighted against the backdrop of a seemingly uniform imbalance [latex]{\cal{I}}^{m}(t)[/latex] as described by [latex]\text{Eq. (3)}[/latex], demonstrating that spatial averaging can obscure critical information about the system’s underlying behavior even in strongly disordered systems with [latex]\Delta = 1[/latex] and [latex]h = 10[/latex].](https://arxiv.org/html/2601.05177v1/x1.png)
![The reflection coefficients-[latex]R[/latex] and [latex]J^{\mathrm{ref,sym}}[/latex], [latex]J^{\mathrm{ref,asym}}[/latex]-exhibit a pronounced dependence on incident angle, varying systematically with on-site potentials and energies, though the radial axis is cropped to enhance clarity of these relationships.](https://arxiv.org/html/2601.05140v1/x10.png)

![The study demonstrates that future iterations of levitated FMTO experiments, leveraging optimized configurations, enhanced vibration isolation, and superconducting shielding, are projected to significantly improve sensitivity to axion-electron coupling-potentially matching or exceeding the constraints currently established by both laboratory-based comagnetometers and astrophysical observations of red-giant cooling and solar axions, as indicated by the projected curves and current limits shown for [latex]g_{aee}[/latex] versus [latex]m_a[/latex].](https://arxiv.org/html/2601.04576v1/prospect.png)
![The measured strength of spin correlations, quantified as [latex] f_{\mathrm{SM}} [/latex], deviates from Standard Model predictions, with statistical uncertainties indicated by inner bars, total experimental uncertainties by middle bars, and comprehensive uncertainties detailed by outer bars-a nuanced assessment of observed phenomena beyond established theoretical frameworks.](https://arxiv.org/html/2601.04649v1/x2.png)
