Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids (2109.05037v6)

Abstract: We present a review of the Sachdev-Ye-Kitaev (SYK) model of compressible quantum many-body systems without quasiparticle excitations, and its connections to various theoretical studies of non-Fermi liquids in condensed matter physics. The review is placed in the context of numerous experimental observations on correlated electron materials. Strong correlations in metals are often associated with their proximity to a Mott transition to an insulator created by the local Coulomb repulsion between the electrons. We explore the phase diagrams of a number of models of such local electronic correlation, employing a dynamical mean field theory in the presence of random spin exchange interactions. Numerical analyses and analytical solutions, using renormalization group methods and expansions in large spin degeneracy, lead to critical regions which display SYK physics. The models studied include the single-band Hubbard model, the $t$-$J$ model and the two-band Kondo-Heisenberg model in the presence of random spin exchange interactions. We also examine non-Fermi liquids obtained by considering each SYK model with random four-fermion interactions to be a multi-orbital atom, with the SYK-atoms arranged in an infinite lattice. We connect to theories of sharp Fermi surfaces without any low-energy quasiparticles in the absence of spatial disorder, obtained by coupling a Fermi liquid to a gapless boson; a systematic large $N$ theory of such a critical Fermi surface, with SYK characteristics, is obtained by averaging over an ensemble of theories with random boson-fermion couplings. Finally, we present an overview of the links between the SYK model and quantum gravity and end with an outlook on open questions.

• The paper demonstrates how the gapless, chaotic dynamics of the SYK model underpin non-Fermi liquid behavior in strongly correlated systems.
• It employs random interactions and large-N limits to derive key features like residual entropy and unconventional transport properties.
• The review bridges theory with experiment, elucidating connections between quantum chaos, strange metal behavior, and compressible electron systems.

Overview of the Sachdev-Ye-Kitaev Models and Non-Fermi Liquids

The paper by Chowdhury et al. provides a comprehensive review of the Sachdev-Ye-Kitaev (SYK) model, a theoretical construct used to paper compressible quantum many-body systems without quasiparticle excitations, extending its connections to non-Fermi liquids in condensed matter physics. The review is grounded in the context of various experimental observations on strongly correlated electron materials, linking theoretical advances to real-world phenomena such as Mott transitions and strange metal behavior.

Key Components of the SYK Models

The Sachdev-Ye-Kitaev (SYK) model is an important theoretical framework because it addresses the absence of quasiparticle excitations in a strongly interacting system, which is contrary to the typical quasiparticle-based paradigm. In the SYK model, the electrons at different sites interact via random couplings, representing a departure from the assumptions of Fermi liquid theory. The model uses self-averaging properties to explore universality and predict dynamical features.

Critical Features and Findings

1. Gapless Nature: The SYK model does not exhibit a gap, inherently leading to a non-Fermi liquid phase characterized by local but non-quasiparticle behavior.
2. Critical Fermi Surface: By introducing random interactions and considering large $N$ limits (where $N$ is the number of sites), the SYK model provides insights into the critical behavior typical of non-Fermi liquids without invoking long-lived quasiparticle excitations.
3. Specific Heat and Entropy: The paper shows how specific heat and extensive entropy calculations can help understand strange metal behavior. One remarkable aspect discussed is the derivation of an extensive entropy in the SYK model that does not vanish as $T \rightarrow 0$, pointing to residual quantum entropic states that defy conventional views.
4. Randomness and Chaos: The SYK model's random interactions introduce chaos and complex dynamics, allowing it to serve as a simplified but effective model for understanding chaotic quantum systems. The absence of spatial localization effects allows the paper of strongly correlated many-body phenomena without interference from localization.
5. Transport Properties: Transport properties, such as electrical conductivity, are addressed by configurations that avoid localized states. They demonstrate regimes where resistivity deviates from the Fermi liquid expectations, potentially linking behaviors like linear-in-temperature resistivity to Planckian scattering rates.

Theoretical and Practical Implications

Chowdhury et al. emphasize several theoretical implications and future directions for studying non-Fermi liquids through the SYK model. The zero-temperature entropy calculations provide crucial insights into ground state degeneracy and anomalous low-energy excitations. Such results open new avenues in exploring quantum chaos, high-temperature superconductivity, and metal-superconductor transitions within a strongly correlated framework.

Speculations on AI Developments

Although not directly related to artificial intelligence, the paper inspires thoughts on how the principles of randomness and non-linear dynamics could inform advanced AI systems. Exploring randomness within SYK models might illuminate novel ways to build machine learning models that handle noise and uncertainty more effectively, particularly in chaotic or non-linear contexts.

Conclusion

The Sachdev-Ye-Kitaev model stands out as a powerful tool for bridging the gap between theoretical predictions and experimental observations in strongly correlated electron systems. While some conjectures and complexities remain unresolved, the paper by Chowdhury et al. sets a foundational base for future research, aiming to unravel more of the deep quantum mechanical properties underpinning non-Fermi liquids.