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arXiv · 2507.07195

Theory of Strongly Correlated Systems: An Introduction to Sachdev-Ye-Kitaev Model

Rishabh Jha
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Abstract

The Sachdev-Ye-Kitaev (SYK) model provides an analytically tractable framework for exotic strongly correlated phases where conventional paradigms like Landau's Fermi liquid theory collapse. This review offers a pedagogical introduction to the SYK physics, highlighting its unique capacity to model \textit{strange metals} -- systems exhibiting linear-in-temperature resistivity, Planckian dissipation, and quasiparticle breakdown. We systematically construct both Majorana and complex fermion variants, transforming them into training grounds for modern many-body physics techniques, for instance, (1) large-$N$ formulations via disorder averaging and replica symmetry, (2) Schwinger-Dyson and Kadanoff-Baym equations, (3) imaginary time Matsubara formulation, (4) real-time dynamics via Keldysh formalism, and the associated (5) non-perturbative Keldysh contour deformations. These tools lay the foundation for equilibrium thermodynamics, quantum chaos, quench dynamics, and transport in the thermodynamic limit, all within a solvable, chaotic quantum system. Intended as a self-contained resource, the review bridges advanced technical machinery to physical insights, with computational implementations provided. Though principally treating the SYK model as a condensed matter laboratory, we also highlight its profound connection to quantum gravity, woven throughout this work, underscoring how this solvable chaotic fermionic model serves as a lens onto black hole thermodynamics and holographic duality.

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BibTeXRIS

Rishabh Jha. 2026-07-06. Theory of Strongly Correlated Systems: An Introduction to Sachdev-Ye-Kitaev Model. https://doi.org/10.1007/978-3-032-20910-8

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