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arXiv · 2511.03460

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

Kohei Fukai·Hosho Katsura
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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.

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Kohei Fukai, Hosho Katsura. 2025-11-05. Integrability of a family of clean SYK models from the critical Ising chain. https://doi.org/10.1103/g4b2-n9c8

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