Multifractality of many-body non-Hermitian skin effect

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.

14 pages, 11 figures

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• Many-Body Non-Hermitian Skin Effect with Exact Steady States in the Dissipative Quantum Link Model
• Non-Hermitian skin effect in fragmented Hilbert spaces of one-dimensional fermionic lattices
• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Limitations of SVD-Based Diagnostics for Non-Hermitian Many-Body Localization with Time-Reversal Symmetry
• Liouvillian skin effects in two-dimensional electron systems at finite temperatures
• Interacting many-body non-Hermitian systems as Markov chains