A bstract We construct a family of near-CFT 1 models with a conserved U(1) charge, whose basic degrees of freedom are canonical bosons. The Sachdev-Ye-Kitaev (SYK) model — the first microscopic model that realizes the near-CFT 1 dynamics — is based on random p -local interactions among fermions. However, a bosonic near-CFT 1 model has remained elusive in the p -local approach because such constructions generally suffer from unwanted orderings at low temperatures. Our construction is based on a recent insight that near-CFT 1 dynamics can quite generally arise if we place a large amount of random fluxes in a many-body Fock space and p -locality is not essential. All such models are essentially solved by chord diagrams regardless of the nature of the underlying degrees of freedom. We further argue that such bosonic models do not suffer from energetic instablities or unwanted low-temperature orderings. For comparison we also consider a second class of charge-conserving models which are based on qubits. The thermodynamic scalings of these models are very similar to those of the double-scaled complex SYK model but are free of certain singularities the latter suffers from. We also show the level statistics of both models are described by random matrix theory universality down to very low energies.
A bstract We construct a family of near-CFT 1 models with a conserved U(1) charge, whose basic degrees of freedom are canonical bosons. The Sachdev-Ye-Kitaev (SYK) model — the first microscopic model that realizes the near-CFT 1 dynamics — is based on random p -local interactions among fermions. However, a bosonic near-CFT 1 model has remained elusive in the p -local approach because such constructions generally suffer from unwanted orderings at low temperatures. Our construction is based on a recent insight that near-CFT 1 dynamics can quite generally arise if we place a large amount of random fluxes in a many-body Fock space and p -locality is not essential. All such models are essentially solved by chord diagrams regardless of the nature of the underlying degrees of freedom. We further argue that such bosonic models do not suffer from energetic instablities or unwanted low-temperature orderings. For comparison we also consider a second class of charge-conserving models which are based on qubits. The thermodynamic scalings of these models are very similar to those of the double-scaled complex SYK model but are free of certain singularities the latter suffers from. We also show the level statistics of both models are described by random matrix theory universality down to very low energies.
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 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 mathbbZ2 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.
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.
Parisi’s hypercube model describes a charged particle hopping on a d -dimensional hypercube with disordered background fluxes in the large d limit. It was noted previously [Jia and Verbaarschot, ] that the hypercube model at leading order in 1/d has the same spectral density as the double-scaled Sachdev-Ye-Kitaev (DS-SYK) model. In this work we identify the set of observables that have the same correlation functions as the DS-SYK model, demonstrating that the hypercube model is an equally good microscopic model for near−AdS2/near−CFT1 holography. Unlike the SYK model, the hypercube model is not p -local. Rather, we note that the shared feature between the two models is that they both have a large amount of disordered but uniform fluxes on their Fock-space graphs, and we propose this is a broader characterization of near−CFT1 microscopics. Moreover, we suggest that the hypercube model can be viewed as the operator growth model of the DS-SYK model. We explain some universality in subleading corrections and relate them to bulk vertices. Finally, we revise a claim made in the aforementioned reference about the existence of a spectral gap. Published by the American Physical Society 2024
We derive the density of states and 2- and 4-point functions of embedded ensembles for both fermions and bosons in the double-scaled limit. It is shown the models are equivalent to the double-scaled Sachdev-Ye-Kitaev model, expanding the double-scaled universality class to include both fermionic and bosonic systems. The models can be solved by introducing the Wick product of non-commuting Gaussian random variables. We show that deriving the Wick product is sufficient for computing the density of states, and properties of the Wick product can be used to compute n-point functions directly in the energy basis. In this context, the Wick product is equivalent to normal ordering of q-oscillators, which leads to the duality between moments of double-scaled models and expectation values in the chord Hilbert space. By considering operator probes as a second set of oscillators, we extend the duality to compute n-point functions. Embedded ensembles are equivalent to complex SYK at fixed charge, and we show working directly with embedded ensembles streamlines the derivations.
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 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.