Transport in spinful non-Hermitian gauge lattices
Abstract
We extend the generalized transfer-matrix method introduced in [H. Ghaemi-Dizicheh, Phys.\ Rev.\ B \textbf{107}, 125155 (2023)] to one-dimensional spinful non-Hermitian tight-binding lattices with matrix-valued Abelian and non-Abelian gauge couplings. We derive a minimal channel-resolved transfer matrix and identify its eigenvalues with the generalized Bloch factors. The same transfer matrix determines the periodic- and open-boundary spectra, generalized 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 poles, zeros, and reflectionlessness, from the directed-amplification factor controlling transmission asymmetry, transparency, and invisibility. For non-Abelian gauge fields, noncommuting link matrices coherently mix the spin sectors, such that four transfer eigenmodes jointly determine the non-Bloch spectrum and transport eigenchannels. We show that this mixing produces spin-hybridized lasing and coherent-perfect-absorption channels, Zeeman-tunable lasing thresholds, and direction-dependent reflectionless transport accompanied by pronounced spin conversion. The resulting boundary-condition criteria describe lasing, coherent perfect absorption, reflectionlessness, transparency, and invisibility, while identifying spin polarization and conversion as experimentally accessible signatures that distinguish Abelian from non-Abelian non-Hermitian transport.
Related
- Representations and n-universality of hermitian lattices over local and number fields
- Stable q-Hermitian coordinate calculus: Capelli--PBW transport, mixed polarization algebra, and localization obstructions
- From cambrian lattices of rank 4 to cambrian lattices of rank 3
- On cube and Cremona rigidity for higher-rank lattices
- Diagonalization of skew-Hermitian dual quaternion matrices and ϕ-Hermitian dual quaternion matrices
BibTeX
@misc{ghaemidizicheh2026transport,
title = {{Transport in spinful non-Hermitian gauge lattices}},
author = {Hamed Ghaemi-Dizicheh and Shahram Dehdashti and Janis Nötzel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40317},
eprint = {2610.40317},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40317},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Transport in spinful non-Hermitian gauge lattices
AU - Hamed Ghaemi-Dizicheh
AU - Shahram Dehdashti
AU - Janis Nötzel
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40317
UR - https://arxiv.org/abs/2610.40317
AB - We extend the generalized transfer-matrix method introduced in [H. Ghaemi-Dizicheh, Phys.\ Rev.\ B \textbf{107}, 125155 (2023)] to one-dimensional spinful non-Hermitian tight-binding lattices with matrix-valued Abelian and non-Abelian gauge couplings. We derive a minimal channel-resolved transfer matrix and identify its eigenvalues with the generalized Bloch factors. The same transfer matrix determines the periodic- and open-boundary spectra, generalized 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 poles, zeros, and reflectionlessness, from the directed-amplification factor controlling transmission asymmetry, transparency, and invisibility. For non-Abelian gauge fields, noncommuting link matrices coherently mix the spin sectors, such that four transfer eigenmodes jointly determine the non-Bloch spectrum and transport eigenchannels. We show that this mixing produces spin-hybridized lasing and coherent-perfect-absorption channels, Zeeman-tunable lasing thresholds, and direction-dependent reflectionless transport accompanied by pronounced spin conversion. The resulting boundary-condition criteria describe lasing, coherent perfect absorption, reflectionlessness, transparency, and invisibility, while identifying spin polarization and conversion as experimentally accessible signatures that distinguish Abelian from non-Abelian non-Hermitian transport.
ER -