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PreprintCC BY 4.0arXiv

Universal Eigenvector Statistics of Non-Hermitian Random Matrices

  • Ze Chen
  • Zhenyu Xiao
  • Shinsei Ryu
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Abstract

Eigenvector overlaps quantify nonorthogonality and govern the response and dynamics of non-Hermitian systems. We extend the universality of non-Hermitian random matrices to the statistics of these overlaps. We obtain analytical expressions for eigenvector overlaps in the spectral bulk and near the origin, covering ten symmetry classes in the limit of large matrix size. Using fermionic replica nonlinear σ models, we relate these overlaps to Hermitian level statistics, symmetry class by symmetry class and topological sector by topological sector. Numerical calculations in various physical models support the universality of the normalized overlaps in the regimes studied. Our work establishes a duality between Hermitian level statistics and non-Hermitian eigenvector overlaps.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026universal,
  title = {{Universal Eigenvector Statistics of Non-Hermitian Random Matrices}},
  author = {Ze Chen and Zhenyu Xiao and Shinsei Ryu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22079},
  eprint = {2609.22079},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22079},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Universal Eigenvector Statistics of Non-Hermitian Random Matrices
AU  - Ze Chen
AU  - Zhenyu Xiao
AU  - Shinsei Ryu
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.22079
UR  - https://arxiv.org/abs/2609.22079
AB  - Eigenvector overlaps quantify nonorthogonality and govern the response and dynamics of non-Hermitian systems. We extend the universality of non-Hermitian random matrices to the statistics of these overlaps. We obtain analytical expressions for eigenvector overlaps in the spectral bulk and near the origin, covering ten symmetry classes in the limit of large matrix size. Using fermionic replica nonlinear σ models, we relate these overlaps to Hermitian level statistics, symmetry class by symmetry class and topological sector by topological sector. Numerical calculations in various physical models support the universality of the normalized overlaps in the regimes studied. Our work establishes a duality between Hermitian level statistics and non-Hermitian eigenvector overlaps.
ER  -