Characterizing Fermionic Non-Gaussianity in the Sachdev-Ye-Kitaev Model via Replica Twist Entropy
Abstract
Understanding the non-equilibrium dynamics of quantum many-body systems plays a central role in modern many-body physics. Intriguing insights emerge from investigating how quantum resources, which are essential for achieving unambiguous quantumness, are generated and spread under chaotic quantum dynamics. In fermionic systems, non-Gaussianity constitutes an important resource beyond entanglement, characterizing the deviation of generic quantum states from free-fermion states. In this Letter, we propose using the \textit{replica twist entropy}, defined through the expectation value of a replica rotation operator with a tunable angle α, as a natural probe of non-Gaussianity in pure fermionic states. After deriving its behavior for typical many-body states, we establish a general framework for analyzing the replica twist entropy in solvable Sachdev-Ye-Kitaev models in the large-N limit. Applying this framework to the dynamics of the thermofield double state, we uncover a novel dynamical phase diagram in the parameter space of α and evolution time t, exhibiting spontaneous Z2 symmetry breaking at α=π/4 and universal cusps as a function of α in the long-time regime. Our results pave the way for studying non-Gaussianity in strongly correlated fermionic systems and reveal a new class of dynamical transitions probed by non-Gaussianity.
Related
- A Zoo of Fermionic Relative Rényi Negativities in the Sachdev-Ye-Kitaev Models
- Computable fermionic non-Gaussianity from the covariance matrix
- Fermionic non-Gaussianity via computable measures and experimentally accessible bounds
- Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity
- Convex-Gaussianity of fermionic Gibbs states in perturbation theory
BibTeX
@misc{sun2026characterizing,
title = {{Characterizing Fermionic Non-Gaussianity in the Sachdev-Ye-Kitaev Model via Replica Twist Entropy}},
author = {Ning Sun and Pengfei Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10123},
eprint = {2610.10123},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10123},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Characterizing Fermionic Non-Gaussianity in the Sachdev-Ye-Kitaev Model via Replica Twist Entropy
AU - Ning Sun
AU - Pengfei Zhang
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.10123
UR - https://arxiv.org/abs/2610.10123
AB - Understanding the non-equilibrium dynamics of quantum many-body systems plays a central role in modern many-body physics. Intriguing insights emerge from investigating how quantum resources, which are essential for achieving unambiguous quantumness, are generated and spread under chaotic quantum dynamics. In fermionic systems, non-Gaussianity constitutes an important resource beyond entanglement, characterizing the deviation of generic quantum states from free-fermion states. In this Letter, we propose using the \textit{replica twist entropy}, defined through the expectation value of a replica rotation operator with a tunable angle α, as a natural probe of non-Gaussianity in pure fermionic states. After deriving its behavior for typical many-body states, we establish a general framework for analyzing the replica twist entropy in solvable Sachdev-Ye-Kitaev models in the large-N limit. Applying this framework to the dynamics of the thermofield double state, we uncover a novel dynamical phase diagram in the parameter space of α and evolution time t, exhibiting spontaneous Z_2 symmetry breaking at α=π/4 and universal cusps as a function of α in the long-time regime. Our results pave the way for studying non-Gaussianity in strongly correlated fermionic systems and reveal a new class of dynamical transitions probed by non-Gaussianity.
ER -