A Zoo of Fermionic Relative Rényi Negativities in the Sachdev-Ye-Kitaev Models

@misc{jiang2026fermionic,
  title = {{A Zoo of Fermionic Relative Rényi Negativities in the Sachdev-Ye-Kitaev Models}},
  author = {Linjing Jiang and Pengfei Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39349},
  eprint = {2610.39349},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39349},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - A Zoo of Fermionic Relative Rényi Negativities in the Sachdev-Ye-Kitaev Models
AU  - Linjing Jiang
AU  - Pengfei Zhang
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39349
UR  - https://arxiv.org/abs/2610.39349
AB  - Quantum entanglement is a fundamental resource that gives rise to correlations with no classical counterpart in strongly correlated fermionic systems. However, its characterization in mixed quantum states remains challenging. Established entanglement diagnostics, such as logarithmic negativity, are computationally demanding in interacting systems, and their evaluation by exact diagonalization is restricted to small system sizes. Meanwhile, conventional Rényi proxies, including twisted and untwisted Rényi negativities, can be positive even for separable states. In this work, we introduce a family of \textit{relative Rényi negativities} that serve as entanglement witnesses. By relating fermionic partial time reversal to the size superoperator, we establish a path-integral representation for these Rényi negativities, enabling their evaluation in thermal states of the Sachdev-Ye-Kitaev (SYK) model and its generalizations via a large-N expansion. Applying this method, we investigate entanglement in both the original SYK model and the Maldacena-Qi coupled SYK model. We identify a special class of relative Rényi negativities which serve as plausible proxies for logarithmic negativity and uncover first-order entanglement transitions that are invisible to simple observables. These results highlight the utility of relative Rényi negativities as probes of mixed-state entanglement in strongly correlated fermionic systems and suggest the existence of a new class of transitions where these negativities serve as free energies.
ER  -