Dimensional spinful non-Hermitian tight-binding lattices with matrix-valued Abelian and non-Abelian gauge couplings are investigated. A minimal channel-resolved transfer matrix is derived, and its eigenvalues correspond to the generalised Bloch factors. The same transfer matrix determines periodic- and open-boundary spectra, a generalised Brillouin zone, skin localization, and finite-sample scattering conditions. In the Abelian limit, the model separates into fixed spin sectors, yielding exact spectral results and closed finite-length transport expressions in terms of Chebyshev polynomials. These results reveal bipolar spin-dependent skin localization and distinguish the reciprocal hopping scale which governs the localization length.

Non-Abelian Interactions Unify Electron Channels Enabling Enhanced Spectral Control and Spin Conversion

College of Undergraduate Studies, collaborating with Technical University of Munich and University of Texas Rio Grande Valley, have demonstrated hybridization of electron channels via non-Abelian interactions. Previously distinct absorption and lasing pathways are now unified, increasing spectral control by a four compared to Abelian systems. This breakthrough enables precise manipulation of electron behaviour within one-dimensional lattices incorporating both “spin” and complex couplings, systems where conventional energy conservation rules do not apply, through Zeeman tuning of lasing thresholds.

Extending an existing transfer matrix method revealed pronounced spin conversion during transport alongside this enhanced control, offering new avenues for strong quantum information processing and novel optical devices. The team adapted a “transfer matrix” technique to analyse electrons moving through lattices with ‘spin’ and complex couplings that break standard energy rules; their work extended established methods in the field. This adaptation demonstrated pronounced spin conversion during electron transport along with improved spectral control.

Four distinct transfer modes were identified as governing electron behaviour within these systems, enabling Zeeman-tunable lasing thresholds, precisely controlled laser light emission via magnetic fields. They also found conditions describing reflectionless transmission, transparency, and even invisibility while observing experimentally accessible signatures of changing spin polarization.

Material Imperfections Impact Engineered Light Control in Complex Systems

While extending existing transfer matrix methods offers unprecedented control over spectral properties, particularly through Zeeman tuning of lasing thresholds, a key question remains: how robust are these effects against imperfections inherent to real materials. Previous work by Ghaemi-Dizicheh laid groundwork for this study; however, that research focused on simpler systems without the thorough incorporation of spin or complex couplings explored here. Acknowledging inevitable deviations from perfect theoretical models is vital because imperfections will influence carefully engineered spectral effects like lasing thresholds and spin conversion rates.

Nevertheless, this exploration provides an essential benchmark for future work, revealing manipulation possibilities for engineered light flow via spin, a property akin to internal magnetism, potentially leading to new optical devices in sensing and information technology within the next decade. Manipulating both ‘spin’, an intrinsic form of angular momentum, and complex couplings breaking standard energy rules allowed researchers to control electron behaviour within one-dimensional lattices; they extended existing mathematical tools used for analysing electron movement through materials. Adapting the “transfer matrix” technique revealed conditions under which unified channels allow absorption or emission as laser light alongside pronounced spin conversion during transport.

This research extends established methods for analyzing electron behavior in one-dimensional systems by incorporating features like spin and complex coupling. The work demonstrates how manipulating these properties allows precise control over electrons moving through a lattice structure, revealing conditions for both absorbing and emitting light, including scenarios of coherent perfect absorption and lasing, along with changes in an electron’s spin polarization. This detailed analysis provides a foundation for understanding similar systems while acknowledging that real materials will have imperfections influencing observed effects.

👉 More information
🗞 Transport in spinful non-Hermitian gauge lattices
✍️ Hamed Ghaemi-Dizicheh (College of Undergraduate Studies); Shahram Dehdashti and Janis Nötzel (Technical University of Munich)
🧠 ArXiv: https://arxiv.org/abs/2610.40317

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