Natural-orbital locking reveals hidden steady-state skin order in Gaussian open fermion chains
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914509918044160 |
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| author | Wang, Y. T. Zhang, X. Z. |
| author_facet | Wang, Y. T. Zhang, X. Z. |
| contents | Nonreciprocal relaxation matrices can have skin-localized right eigenmodes, but their imprint on a mixed steady state is not fixed by the density profile alone. We develop an exact steady-state theory for number-conserving Gaussian fermion chains and show that the dominant natural orbital of the correlation matrix provides a mode-resolved diagnostic of hidden skin order. The steady-state correlator admits a biorthogonal decomposition in terms of the left and right eigenmodes of the relaxation matrix $X$ and the source matrix $Y$. This formula separates three ingredients: slow rapidity denominators, source loading by left eigenmodes, and real-space geometry from right eigenmodes. For a local pump, the pump position is read by the left modes, whereas the selected profile is drawn by the right modes. In a single-slow-mode regime, the dominant natural orbital locks to the Euclidean-normalized slow right mode. The density can follow the same boundary trend, but it is a less selective incoherent sum over occupied natural orbitals. We verify this selection law in a nonreciprocal Hatano--Nelson chain and show that, in a nonreciprocal SSH chain, the selected natural orbital crosses over from a topological edge candidate to a slow bulk-skin candidate. These results identify natural-orbital locking as a steady-state diagnostic of nonreciprocal localization in Gaussian open fermion chains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24121 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Natural-orbital locking reveals hidden steady-state skin order in Gaussian open fermion chains Wang, Y. T. Zhang, X. Z. Quantum Physics Nonreciprocal relaxation matrices can have skin-localized right eigenmodes, but their imprint on a mixed steady state is not fixed by the density profile alone. We develop an exact steady-state theory for number-conserving Gaussian fermion chains and show that the dominant natural orbital of the correlation matrix provides a mode-resolved diagnostic of hidden skin order. The steady-state correlator admits a biorthogonal decomposition in terms of the left and right eigenmodes of the relaxation matrix $X$ and the source matrix $Y$. This formula separates three ingredients: slow rapidity denominators, source loading by left eigenmodes, and real-space geometry from right eigenmodes. For a local pump, the pump position is read by the left modes, whereas the selected profile is drawn by the right modes. In a single-slow-mode regime, the dominant natural orbital locks to the Euclidean-normalized slow right mode. The density can follow the same boundary trend, but it is a less selective incoherent sum over occupied natural orbitals. We verify this selection law in a nonreciprocal Hatano--Nelson chain and show that, in a nonreciprocal SSH chain, the selected natural orbital crosses over from a topological edge candidate to a slow bulk-skin candidate. These results identify natural-orbital locking as a steady-state diagnostic of nonreciprocal localization in Gaussian open fermion chains. |
| title | Natural-orbital locking reveals hidden steady-state skin order in Gaussian open fermion chains |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.24121 |