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Biorthogonal Doublon–Holon Dipole Tomography for Collective Skin Localization in Non-Reciprocal Spin-Fermion Chains

Vincent Marks1, R. A. Sulaiman1
1University of Surrey, Guildford GU2 7XH, Surrey, UK
Vincent Marks
University of Surrey, Guildford GU2 7XH, Surrey, UK
R. A. Sulaiman
University of Surrey, Guildford GU2 7XH, Surrey, UK

Abstract

The study of non-Hermitian lattice models has emerged as indispensable to the characterization of engineered quantum materials, arrays of optical elements, electric circuits, and cold atomic simulators where dissipative processes or non-reciprocal transport modify the connection between bulk band structure and surface states. When considering interacting fermionic systems, the non-Hermitian skin effect can no longer be detected through total charge accumulation, since correlations lead to the formation of composite charge defects that affect the mobile degrees of freedom. Here we introduce a novel biorthogonal doublon-holon dipole tomography technique for detecting correlated skin localization effects in a non-reciprocal spin-1/2 Hubbard chain. The procedure breaks down each individual eigenstate into left-right normalized doublon density, holon density, defect dipole polarization, quasiparticle separation, connected doublon-holon covariance, and flux dependence of spectral complexity. The procedure is used to analyze half-filled and holon-doped Hubbard chains at \(L=8\), \(N=8\), \(N=7\), both periodic and open boundary conditions, \(A=0.3\), representative couplings \(U/t=0\) and \(U/t=10\), and \(U/t\rightarrow20\) interaction scans. Our findings show that in the half-filled no-pair Mott sector, charge polarization is maintained at a weak level, while in finite doublon-holon sectors, boundary stretched dipole textures appear and increase in intensity proportionally to the charge defects. As interactions are turned on, the smooth weak-correlation imbalance is replaced by a staircase of states ordered according to doublon-holon occupancy; in the case of the doped chain, an unpaired holon provides an additional boundary-active channel, resulting in a response biased towards an odd integer hierarchy. Flux-torsion spectroscopy establishes a connection between the texture and complex eigenvalue loops, allowing us to identify exceptional state reconfiguration events where complex eigenvalue branches turn real. These tools enable an excitation resolved exploration of collective non-Hermitian skin effect physics in interacting quantum materials.

Keywords: non-Hermitian quantum materials, non-reciprocal Hubbard chain, doublon–holon excitation, collective skin effect, biorthogonal tomography, point-gap topology, engineered materials
Copyright © 2024 Vincent Marks, R. A. Sulaiman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.