We analyze a model of qubits that we argue has an emergent quantum gravitational description similar to the fermionic Sachdev-Ye-Kitaev (SYK) model. The model we consider is known as the quantum
q-spin model because it features
q-local interactions between qubits. It was previously studied as a model of a quantum spin glass, and while we find that the model is glassy for
q=2,q=3, and likely
q=4, we also find evidence for previously unexpected SYK-like behavior for the quenched free energy down to the lowest temperatures for $q\ensuremath{\ge}5$. This SYK-like physics includes power-law correlation functions and an extensive low-temperature entropy, so we refer to the model as Spin SYK. The model is generic in that it includes all possible
q-body couplings, lacks most symmetries, and has no spatial structure, so our results can be construed as establishing a certain ubiquity of quantum holography in systems dominated by many-body interactions. Furthermore, we discuss a generalized family of models that includes Spin SYK and which provably exhibit SYK-like physics in the solvable limit of large local Hilbert space dimension. We also comment on the implications of a bosonic system with SYK-like properties for the study of holography, Hamiltonian complexity, and related topics.
We analyze a model of qubits which we argue has an emergent quantum gravitational description similar to the fermionic Sachdev-Ye-Kitaev (SYK) model. The model we consider is known as the quantum
q-spin model because it features
q-local interactions between qubits. It was previously studied as a model of a quantum spin glass, and while we find that the model is glassy for
q=2,
q=3, and likely
q=4, we also find evidence for previously unexpected SYK-like behavior for the quenched free energy down to the lowest temperatures for
q≥5. This SYK-like physics includes power-law correlation functions and an extensive low temperature entropy, so we refer to the model as Spin SYK. The model is generic in that it includes all possible
q-body couplings, lacks most symmetries, and has no spatial structure, so our results can be construed as establishing a certain ubiquity of quantum holography in systems dominated by many-body interactions. Furthermore, we discuss a generalized family of models which includes Spin SYK and which provably exhibit SYK-like physics in the solvable limit of large local Hilbert space dimension. We also comment on implications of a bosonic system with SYK-like properties for the study of holography, Hamiltonian complexity, and related topics.
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.
We briefly introduce and review the Sachdev-Ye-Kitaev (SYK) model. This model exhibits quenched disorder, and many quantities, like the Euclidean path integral, are computed as an average over disorder or an average over many different unitary theories corresponding to different realizations of the disorder couplings. This places the interpretation of the Euclidean path integral as a thermal partition function under scrutiny, which we promptly investigate. We reach he seeming conclusion that the Euclidean path integral indeed does not support a Hilbert space interpretation, which is corroborated by other investigations in the literature. We then move one dimension higher, to two-dimensional Jackiw-Teitelboim (JT) gravity, investigating its salient features and most importantly, the problem of Hilbert space factorization. This puzzle implies that, due to constraints coming from gauge symmetry, a bulk gravitational theory cannot be dual to a theory with a tensor-product structure on disconnected boundary components. We then briefly introduce and review spin glasses, and review the investigations into the presence of a spin glass phase in the SYK model. Finally, we discuss some natural outgrowths of ideas presented in this thesis
The Sachdev-Ye-Kitaev (SYK) model is a solvable model of a many-body quantum system that has stimulated interest in both condensed matter physics and quantum gravity. This review focuses on the insights provided by the SYK model, which has no quasiparticle excitations, into the physics of Planckian non-Fermi-liquid metals. This is discussed for a range of strongly correlated models and in relation to experiments on strongly correlated materials. Also included is a discussion of recent developments regarding the connections between the SYK model and the quantum theory of black holes.