Full-spectrum pairwise coalescence of eigenstates in a class of non-Hermitian Hamiltonians

• URL: http://arxiv.org/abs/2411.06305v1
• Date: Sat, 09 Nov 2024 23:00:24 GMT
• Title: Full-spectrum pairwise coalescence of eigenstates in a class of non-Hermitian Hamiltonians
• Authors: Yusuf H. Erdogan, Masudul Haque,
• Abstract summary: We consider non-Hermitian tight-binding one-dimensional Hamiltonians. We show that imposing a certain symmetry causes all eigenvalues to pair up and the corresponding eigenstates to coalesce in pairs.
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• Abstract: We consider non-Hermitian tight-binding one-dimensional Hamiltonians and show that imposing a certain symmetry causes all eigenvalues to pair up and the corresponding eigenstates to coalesce in pairs. This Pairwise Coalescence (PC) is an enhanced version of an exceptional point -- the complete spectrum pairs up, not just one pair of eigenstates. The symmetry is that of reflection excluding the central two sites, and allowing flipping of non-reciprocal hoppings (``generalized off-center reflection symmetry''). Two simple examples of PC exist in the literature -- our construction encompasses these examples and extends them to a vast class of Hamiltonians. We study several families of such Hamiltonians, extend to cases of full-spectrum higher-order coalescences, and show how the PC point corresponds to amplified non-orthogonality of the eigenstates and enhanced loss of norm in time evolution.

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