Non-Hermitian Skin Effect Along Hyperbolic Geodesics

Fuente: arXiv
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Main Authors: Shen, Ruizhe, Chan, Wei Jie, Lee, Ching Hua
Format: Preprint
Published: 2024
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author Shen, Ruizhe
Chan, Wei Jie
Lee, Ching Hua
author_facet Shen, Ruizhe
Chan, Wei Jie
Lee, Ching Hua
contents Recently, it has been revealed that a variety of novel phenomena emerge in hyperbolic spaces, while non-Hermitian physics has significantly enriched the landscape of condensed matter physics. Building on these developments, we construct a geodesic-based method to study the non-Hermitian skin effect (NHSE) in non-reciprocal hyperbolic lattices. Additionally, we develop a geodesic-periodic boundary condition (geodesic-PBC), akin to the Euclidean periodic boundary condition (PBC), that complements its open boundary condition. Importantly, we find that the non-reciprocal directionality within a hyperbolic regular polygon and the geodesic-based boundary determine the spectral sensitivity, and hence, the NHSE. Unlike in Euclidean models, however, we must utilize boundary localization to distinguish non-trivial skin modes from their trivial boundary counterpart due to the extensive boundary volume of hyperbolic lattices. We also relate the spatial density profile with the finite-size scaling of hyperbolic lattices. These aspects highlight the profound impact of hyperbolic geometry on non-Hermitian systems and offer new perspectives on the intricate relationship between the geometric characteristics of hyperbolic lattices and non-Hermitian physics.
format Preprint
id arxiv_https___arxiv_org_abs_2410_15278
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Non-Hermitian Skin Effect Along Hyperbolic Geodesics
Shen, Ruizhe
Chan, Wei Jie
Lee, Ching Hua
Other Condensed Matter
Mesoscale and Nanoscale Physics
Recently, it has been revealed that a variety of novel phenomena emerge in hyperbolic spaces, while non-Hermitian physics has significantly enriched the landscape of condensed matter physics. Building on these developments, we construct a geodesic-based method to study the non-Hermitian skin effect (NHSE) in non-reciprocal hyperbolic lattices. Additionally, we develop a geodesic-periodic boundary condition (geodesic-PBC), akin to the Euclidean periodic boundary condition (PBC), that complements its open boundary condition. Importantly, we find that the non-reciprocal directionality within a hyperbolic regular polygon and the geodesic-based boundary determine the spectral sensitivity, and hence, the NHSE. Unlike in Euclidean models, however, we must utilize boundary localization to distinguish non-trivial skin modes from their trivial boundary counterpart due to the extensive boundary volume of hyperbolic lattices. We also relate the spatial density profile with the finite-size scaling of hyperbolic lattices. These aspects highlight the profound impact of hyperbolic geometry on non-Hermitian systems and offer new perspectives on the intricate relationship between the geometric characteristics of hyperbolic lattices and non-Hermitian physics.
title Non-Hermitian Skin Effect Along Hyperbolic Geodesics
topic Other Condensed Matter
Mesoscale and Nanoscale Physics
url https://arxiv.org/abs/2410.15278