The Sachdev-Ye-Kitaev Model and Matter Without Quasiparticles

Abstract

This thesis is devoted to the study of Sachdev-Ye-Kitaev (SYK) models, which describe matter without quasiparticles. The SYK model is an exactly solvable model that is hoped to bring insights into the understanding of strongly correlated materials. The main part discusses different aspects of SYK models. Chapter 2 presents numerical studies of the SYK models, shows its non-Fermi liquid nature and verifies the analytical predictions on two-point function and thermal entropies. Chapter 3 considers the thermodynamic and transport properties of the complex SYK models in higher dimensional generalizations, we show some universal relations obtained from SYK models which are consistent with holographic theories. Chapter 4 discusses a supersymmetric generalization of the SYK model. We show a different a scaling from the normal SYK model both analytically and numerically. We also discuss a different origin of the extensive zero temperature entropy in $\mathcal{N}=2$ theory. Chapter 5 considers a continuous set of boson-fermion SYK models with a tunable low-energy scaling dimension. From the explicit computation of out of time ordered correlators, we find the theory is less chaotic in the free fermion limit. Chapter 6 describes the phases of a solvable $t$-$J$ model of electrons with an SYK-like form. We find a $\mathbb{Z}_2$ fractionalization picture where the deconfined phase is similar to the pseudo gap regime of underdoped cuprates, while the `quasi-Higgs' phase is similar to the metallic phase of overdoped cuprates.