Introduction to Sachdev-Ye-Kitaev Model: A Strongly Correlated System Perspective

TL;DR

This paper introduces the Sachdev-Ye-Kitaev (SYK) model as a solvable framework for studying strongly correlated quantum systems, highlighting its applications in condensed matter physics and connections to quantum gravity and holography.

Contribution

It provides a comprehensive pedagogical review of the SYK model, including its variants, analytical techniques, and physical insights, bridging condensed matter and quantum gravity.

Findings

SYK model captures strange metal behavior with linear-in-temperature resistivity.

Analytical tools like large-N and Schwinger-Dyson equations are systematically developed.

The model reveals deep connections between quantum chaos, thermodynamics, and holography.

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.