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arXiv:2402.17824

Quantum spin glasses and Sachdev-Ye-Kitaev models

Subir Sachdev A

Published Feb 27, 2024• 1 citation
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Abstract

A brief survey of some random quantum models with infinite-range couplings is presented, ranging from the quantum Ising model to the Sachdev-Ye-Kitaev model. The Sachdev-Ye-Kitaev model was the first to realize an extensive zero temperature entropy without requiring an exponentially large ground state degeneracy. This phenomenon is closely linked to the absence of a particle-like interpretation of its low energy spectrum--its spectral functions are not those of bosons or fermions but are instead "Planckian", meaning they are universal functions of energy/temperature. A remarkable consequence of these properties is that the SYK model provides an effective low energy theory of non-supersymmetric charged or rotating black holes in 3+1 dimensions, leading to new results on the density of many-body quantum states of such black holes. For applications to non-quasiparticle metallic states of quantum materials, an extension of the SYK model, known as the two-dimensional Yukawa-Sachdev-Ye-Kitaev model, is required. The 2dYSYK model describes quantum phase transitions in metals with spatial inhomogeneity in the position of the quantum critical point. This extension has led to a universal theory of the strange metal state observed in numerous correlated electron compounds, including copper-oxide based high temperature superconductors.

DOI
10.48550/arxiv.2402.17824

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A brief survey of some random quantum models with infinite-range couplings is presented, ranging from the quantum Ising model to the Sachdev-Ye-Kitaev model. The Sachdev-Ye-Kitaev model was the first to realize an extensive zero temperature entropy without requiring an exponentially large ground state degeneracy. This phenomenon is closely linked to the absence of a particle-like interpretation of its low energy spectrum--its spectral functions are not those of bosons or fermions but are instead "Planckian", meaning they are universal functions of energy/temperature. A remarkable consequence of these properties is that the SYK model provides an effective low energy theory of non-supersymmetric charged or rotating black holes in 3+1 dimensions, leading to new results on the density of many-body quantum states of such black holes. For applications to non-quasiparticle metallic states of quantum materials, an extension of the SYK model, known as the two-dimensional Yukawa-Sachdev-Ye-Kitaev model, is required. The 2dYSYK model describes quantum phase transitions in metals with spatial inhomogeneity in the position of the quantum critical point. This extension has led to a universal theory of the strange metal state observed in numerous correlated electron compounds, including copper-oxide based high temperature superconductors.
This review is a contribution to a book dedicated to the memory of Michael E. Fisher. The first example of a quantum many body system not expected to have any quasiparticle excitations was the Wilson-Fisher conformal field theory. The absence of quasiparticles can be established in the compressible, metallic state of the Sachdev-Ye-Kitaev model of fermions with random interactions. The solvability of the latter model has enabled numerous computations of the non-quasiparticle dynamics of chaotic many-body states, such as those expected to describe quantum black holes. We review thermodynamic properties of the SYK model, and describe how they have led to an understanding of the universal structure of the low energy density of states of charged black holes without low energy supersymmetry.
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 ttt-JJJ 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 NNN 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.
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.\nThe 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 mathcalN=2\\mathcal{N}=2mathcalN=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 ttt-JJJ model of electrons with an SYK-like form. We find a mathbbZ2\\mathbb{Z}_2mathbbZ2​ 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.
The two-dimensional Yukawa-Sachdev-Ye-Kitaev (2D-YSYK) model provides a universal theory of quantum phase transitions in metals in the presence of quenched random spatial fluctuations in the local position of the quantum critical point. It has a Fermi surface coupled to a scalar field by spatially random Yukawa interactions. We present full numerical solutions of a self-consistent disorder averaged analysis of the 2D-YSYK model in both the normal and superconducting states, obtaining electronic spectral functions, frequency-dependent conductivity, and superfluid stiffness. Our results reproduce key aspects of observations in the cuprates as analyzed by Michon et al. [Nat. Commun. 14, 3033 (2023)NCAOBW2041-172310.1038/s41467-023-38762-5]. We also find a regime of increasing zero temperature superfluid stiffness with decreasing superconducting critical temperature, as is observed in bulk cuprates.