Integrability of a family of clean SYK models from the critical Ising chain
Kohei Fukai, Hosho Katsura
We establish the integrability of a family of Sachdev-Ye-Kitaev (SYK) models with uniform $p$-body interactions. We derive the R-matrix and mutually commuting transfer matrices that generate the Hamiltonians of these models, and obtain their exact eigenspectra and eigenstates. Remarkably, the R-matrix is that of the critical transverse-field Ising chain. This work reveals an unexpected connection between the SYK model, central to many-body quantum chaos, and the critical Ising chain, a cornerstone of statistical mechanics.
cond-mat.stat-mechCross-listedarXiv:2511.03460•Physical review. B./Physical review. B•Nov 6, 2025•1 citation