Theory of Strongly Correlated Systems

Theory of Strongly Correlated Systems

An Introduction to Sachdev-Ye-Kitaev Model

von Rishabh Jha

This book provides an analytically tractable framework for exploring strongly correlated quantum systems beyond conventional paradigms such as Landau’s Fermi liquid theory. This book offers a pedagogical and self-contained introduction to SYK physics, emphasizing its role in describing strange metals —systems with linear-in-temperature resistivity, Planckian dissipation, and quasiparticle breakdown.

Beginning with an invitation to the SYK paradigm, the text develops both Majorana and complex fermion variants and presents modern many-body tools including large-N formulations, Schwinger–Dyson and Kadanoff–Baym equations, Matsubara and Keldysh formalisms, and nonperturbative contour deformations. These methods are applied to study equilibrium thermodynamics, quantum chaos, quench dynamics, and transport phenomena.

Extensive appendices provide mathematical background and Mathematica® implementations for critical exponents, conductivity, and transport across temperature regimes.

Bridging analytical depth with computational practice, this book also highlights the deep connections between the SYK model, black hole thermodynamics, and holographic duality, illustrating how a simple fermionic model offers insight into both condensed matter systems and quantum gravity. It serves as an essential resource for advanced students and researchers in strongly correlated and holographic quantum matter.

This book provides an analytically tractable framework for exploring strongly correlated quantum systems beyond conventional paradigms such as Landau’s Fermi liquid theory. This book offers a pedagogical and self-contained introduction to SYK physics, emphasizing its role in describing strange metals —systems with linear-in-temperature resistivity, Planckian dissipation, and quasiparticle breakdown.

Beginning with an invitation to the SYK paradigm, the text develops both Majorana and complex fermion variants and presents modern many-body tools including large-N formulations, Schwinger–Dyson and Kadanoff–Baym equations, Matsubara and Keldysh formalisms, and nonperturbative contour deformations. These methods are applied to study equilibrium thermodynamics, quantum chaos, quench dynamics, and transport phenomena.

Extensive appendices provide mathematical background and Mathematica® implementations for critical exponents, conductivity, and transport across temperature regimes.

Bridging analytical depth with computational practice, this book also highlights the deep connections between the SYK model, black hole thermodynamics, and holographic duality, illustrating how a simple fermionic model offers insight into both condensed matter systems and quantum gravity. It serves as an essential resource for advanced students and researchers in strongly correlated and holographic quantum matter.

Highlights

• Offers a complete, pedagogical gateway to SYK physics Covers everything: equilibrium, non-equilibrium, transport, and quantum chaos in a solvable framework Brings together large‑N methods, real‑ and imaginary‑time formalisms, and Mathematica implementations

Über den Autor

Rishabh Jha has worked at the frontiers of high-energy physics and condensed matter theory, with publications spanning black hole thermodynamics to exotic quantum phases of matter. He obtained his doctorate with the highest distinction and the Latin honor summa cum laude for modelling and charting the phase diagram of exotic phases, where he was also the recipient of outstanding doctoral thesis prize by the Dr. Berliner – Dr. Ungewitter foundation. His work on the SYK model has unraveled surprising universalities, particularly concerning the nature of chaos and phase transitions in disordered and nonlocal theories. Intriguingly, the behavior of these exotic strange metals also admits holographic dualities to classical gravity theories in one higher dimension. He has previously authored review lecture notes on the Hamiltonian formulation of general relativity and homogeneous cosmologies, published with SciPost. With significant experience in both teaching and research, he was awarded the DAAD Prize for outstanding international students by the German Academic Exchange Service for his “excellent achievements plus commitment to teaching, supervising, and supporting.”