Integrability of a family of clean SYK models from the critical Ising chain

Kohei Fukai; Hosho Katsura

doi:10.1103/g4b2-n9c8

Integrability of a family of clean SYK models from the critical Ising chain

Kohei Fukai ^1,* and Hosho Katsura ^1,2,3,†

¹Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
²Institute for Physics of Intelligence, The University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan
³Trans-Scale Quantum Science Institute, The University of Tokyo, 7-3-1, Hongo, Tokyo 113-0033, Japan

^*Contact author: kohei.fukai@phys.s.u-tokyo.ac.jp
^†Contact author: katsura@phys.s.u-tokyo.ac.jp

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Phys. Rev. B 113, 115107 – Published 4 March, 2026

DOI: https://doi.org/10.1103/g4b2-n9c8

Abstract

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.

Physical Review B

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Integrability of a family of clean SYK models from the critical Ising chain

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Integrability of a family of clean SYK models from the critical Ising chain

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