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Non-hermiticity of evolution operators appears in a wide range of physics, from classical to quantum systems [1]. Non-Hermiticity enables macroscopic accumulation of bulk states, named non-Hermitian skin effects [2]. They are well-established for single-particle systems, but their proper characterization for general systems is elusive.

In this talk, we propose a general criterion of non-Hermitian skin effects, which works for any finite-dimensional system evolved by a linear operator [3]. The applicable systems include many-body systems. A system meeting the criterion exhibits enhanced non-normality of the evolution operator [4], 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. In particular, we investigate the interacting Hatano-Nelson model to illustrate this concept, and find a difference in the behavior of non-normality in the single-particle case and in the many-body case. We also discuss the Fock space skin effect-induced slow transient dynamics, which gives an experimental signal for the Fock space skin effect.

[1] Y. Ashida, Z. Gong, and M. Ueda, Adv. Phys. 69, 249, (2020).

[2] S. Yao and Z. Wang, Phys. Rev. Lett. 121, 086803 (2018).

[3] K. Shimomura and M. Sato, arXiv:2403.13595 (2024).

[4] Y. O. Nakai, N. Okuma, D. Nakamura, K. Shimomura, and M. Sato, Phys. Rev. B 109, 144203 (2024).

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