The Signal
Fudan Researchers Find Hidden Entanglement Transitions in SYK Models
Linjing Jiang and Pengfei Zhang of Fudan University introduce fermionic relative Rényi negativities to detect mixed-state entanglement in Sachdev–Ye–Kitaev models. Their large-N calculations reveal first-order transitions that simple observ
Quantum.world Team · Written with AI · fact-checked ·
Simple observables can miss abrupt changes in entanglement in theoretical fermion systems; a new family of measures developed by Linjing Jiang and Pengfei Zhang is designed to expose them. In a paper submitted to arXiv on October 29, the Fudan University researchers report first-order entanglement transitions in Sachdev–Ye–Kitaev (SYK) models, including transitions that do not show up in conventional observables. Their results come from large-N calculations, not an experiment on a material.
Why familiar Rényi measures can mislead
Mixed quantum states are difficult to assess because ordinary subsystem entropy combines entanglement with thermal effects. Logarithmic negativity can certify entanglement, but the authors say calculating it directly in interacting systems is demanding and exact diagonalization limits calculations to small systems. Rényi negativities offer computationally useful alternatives, yet standard versions can be positive even for separable states, so a positive value alone does not establish entanglement.
Jiang and Zhang construct relative Rényi negativities from different orderings of a partially time-reversed density matrix and its Hermitian conjugate. They define the quantities so they vanish for separable states; a positive value therefore witnesses mixed-state entanglement. The paper’s abstract states: “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.” Linjing Jiang and Pengfei Zhang, Fudan University
A size operator turns the test into a path integral
The method links fermionic partial time reversal to a “size superoperator,” which tracks the number of Majorana operators in a term. That connection lets the authors express the new quantities as path integrals at fixed integer replica number, without requiring a replica limit for the calculation. They then use a large-N expansion to study thermal states in the original SYK model and the coupled Maldacena–Qi model.
The measures do not all behave alike. In the single-SYK calculations, the authors find that a “minimal-deviation” subset decreases as temperature rises, a trend that supports its use as a proxy for logarithmic negativity. Other members can vary non-monotonically with temperature. At fourth Rényi order, one quantity develops competing saddle-point solutions; the switch in which solution dominates produces a first-order transition that the paper says is absent from simple observables.
Two transitions emerge in the coupled model
The Maldacena–Qi model joins two SYK systems through a direct coupling that entangles their left and right sides. In the weak-coupling regime, the relative negativities studied by Jiang and Zhang display two successive first-order transitions as temperature falls. The first is tied to the model’s thermal transition; the second arises from the relative-negativity calculation itself, as a different saddle becomes dominant.
For a coupling ratio μ/J of 0.1, the paper places the first transition in the second-order relative negativity at approximately βJ = 14, where β is inverse temperature and J sets the interaction scale. The authors connect the second transition to changes in correlations between replicas in the calculation. These are theoretical transitions in a controlled model, not evidence of a newly observed phase in a laboratory system.
A diagnostic, not yet an experimental result
The work’s contribution is a way to distinguish entanglement-sensitive transitions from changes visible in ordinary thermodynamic quantities. Its proposed measures are witnesses when positive, but only some show the temperature dependence the authors expect of a useful proxy for logarithmic negativity. The paper also relies on a large-N treatment; its findings establish behavior within that framework, not a measurement in a finite device or material.
Jiang and Zhang conclude that comparing these relative negativities can expose changes in the dominant mathematical saddle—and hence in the modeled entanglement—that simpler observables conceal. In their coupled-SYK example, the calculation resolves two transitions, with the first near βJ = 14 at μ/J = 0.1.