Non-Hermitian Multipole Skin Effects Challenge Localization

• URL: http://arxiv.org/abs/2504.10580v2
• Date: Mon, 19 May 2025 18:00:28 GMT
• Title: Non-Hermitian Multipole Skin Effects Challenge Localization
• Authors: Jacopo Gliozzi, Federico Balducci, Taylor L. Hughes, Giuseppe De Tomasi,
• Abstract summary: We study the effect of quenched disorder on the non-Hermitian skin effect in systems that conserve a U(1) charge.<n>In particular, we generalize the Hatano-Nelson argument for a localization transition in disordered, non-reciprocal systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the effect of quenched disorder on the non-Hermitian skin effect in systems that conserve a U(1) charge and its associated multipole moments. In particular, we generalize the Hatano-Nelson argument for a localization transition in disordered, non-reciprocal systems to the interacting case. When only U(1) charge is conserved, we show that there is a transition between a skin effect phase, in which charges cluster at a boundary, and a many-body localized phase, in which charges localize at random positions. In the dynamics of entanglement, this coincides with an area to volume law transition. For systems without boundaries, the skin effect becomes a delocalized phase with a unidirectional current. If dipoles or higher multipoles are conserved, we show that the non-Hermitian skin effect remains stable to arbitrary disorder. Counterintuitively, the system is therefore always delocalized under periodic boundary conditions, regardless of disorder strength.

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