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arXiv · 2401.08304

Multifractality of many-body non-Hermitian skin effect

Shu Hamanaka·Kohei Kawabata
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Abstract

The non-Hermitian skin effect, anomalous localization of an extensive number of eigenstates induced by nonreciprocal dissipation, plays a pivotal role in non-Hermitian topology and significantly influences the open quantum dynamics. However, its genuinely quantum characterization in many-body systems has yet to be developed. Here, we elucidate that the skin effect manifests itself as multifractality in the many-body Hilbert space. This multifractality does not accompany the single-particle skin effect and hence is intrinsic to the many-body skin effect. Furthermore, we demonstrate that the many-body skin effect coexists with spectral statistics of random matrices, in contrast to multifractality associated with the many-body localization, which necessitates the absence of ergodicity. We also illustrate multifractality caused by the Liouvillian skin effect in Markovian open quantum systems. Our work establishes a defining characterization of the non-Hermitian skin effect and uncovers a fundamental relationship between multifractality and ergodicity in open quantum many-body systems.

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Shu Hamanaka, Kohei Kawabata. 2025-01-23. Multifractality of many-body non-Hermitian skin effect. https://doi.org/10.1103/physrevb.111.035144

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