General criterion for non-Hermitian skin effects and Application: Fock space skin effects in many body systems

• URL: http://arxiv.org/abs/2403.13595v3
• Date: Mon, 30 Sep 2024 01:53:05 GMT
• Title: General criterion for non-Hermitian skin effects and Application: Fock space skin effects in many body systems
• Authors: Kenji Shimomura, Masatoshi Sato,
• Abstract summary: Non-Hermitian skin effects are well-established for single-particle systems, but their proper characterization for general systems is elusive. We propose a general criterion of non-Hermitian skin effects, which works for any finite-dimensional system evolved by a linear operator. Applying the criterion, we discover a new type of non-Hermitian skin effect in many-body systems, which we dub the Fock space skin effect.
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• Abstract: Non-Hermiticity enables macroscopic accumulation of bulk states, named non-Hermitian skin effects. The non-Hermitian skin effects are well-established for single-particle systems, but their proper characterization for general systems is elusive. Here, we propose a general criterion of non-Hermitian skin effects, which works for any finite-dimensional system evolved by a linear operator. The applicable systems include many-body systems and network systems. A system meeting the criterion exhibits enhanced non-normality of the evolution operator, accompanied by exceptional characteristics intrinsic to non-Hermitian systems. Applying the criterion, we discover a new type of non-Hermitian skin effect in many-body systems, which we dub the Fock space skin effect. We also discuss the Fock space skin effect-induced slow dynamics, which gives an experimental signal for the Fock space skin effect.

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