Integrability of a family of clean SYK models from the critical Ising chain
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.
Fields of Study & Subjects
Quantum many-body systems
Algebraic structures and combinatorial models
Theoretical and Computational Physics
Publication details
- Journal / source
- Physical review. B./Physical review. B
- Publisher
- American Physical Society (APS)
- Volume
- 113
- Issue
- 11
- Publication date
- 3 February 2026
- Language
- EN