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Main Authors: Erdogan, Yusuf H., Haque, Masudul
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2411.06305
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author Erdogan, Yusuf H.
Haque, Masudul
author_facet Erdogan, Yusuf H.
Haque, Masudul
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2411_06305
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Supercharging exceptional points: Full-spectrum pairwise coalescence in non-Hermitian systems
Erdogan, Yusuf H.
Haque, Masudul
Quantum Physics
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.
title Supercharging exceptional points: Full-spectrum pairwise coalescence in non-Hermitian systems
topic Quantum Physics
url https://arxiv.org/abs/2411.06305