Solvable Sachdev-Ye-Kitaev Models in Higher Dimensions: From Diffusion to Many-Body Localization

Defect Conformal Field Theory from Sachdev-Ye-Kitaev Interactions

The coupling between defects and extended critical degrees of freedom gives rise to the intriguing theory known as defect conformal field theory (CFT). In this work, we introduce a novel family of boundary and interface CFTs by coupling N Majorana chains with SYK_{q} interactions at the defect. Our analysis reveals that the interaction with q=2 constitutes a new marginal defect. Employing a versatile saddle-point method, we compute unique entanglement characterizations, including the g function and effective central charge, of the defect CFT. Furthermore, we analytically evaluate the transmission coefficient using CFT techniques. Surprisingly, the transmission coefficient deviates from the universal relation with the effective central charge across the defect at the large N limit, suggesting that our defect CFT extends beyond all known examples of Gaussian defect CFT.

From Chaos to Integrability in Double Scaled Sachdev-Ye-Kitaev Model via a Chord Path Integral

We study thermodynamic phase transitions between integrable and chaotic dynamics. We do so by analyzing models that interpolate between the chaotic double scaled Sachdev-Ye-Kitaev (SYK) and the integrable p-spin systems, in a limit where they are described by chord diagrams. We develop a path integral formalism by coarse graining over the diagrams, which we use to argue that the system has two distinct phases: one is continuously connected to the chaotic system, and the other to the integrable. They are separated by a line of first order transition that ends at some finite temperature.

Exponential Ramp in the Quadratic Sachdev-Ye-Kitaev Model

A long period of linear growth in the spectral form factor provides a universal diagnostic of quantum chaos at intermediate times. By contrast, the behavior of the spectral form factor in disordered integrable many-body models is not well understood. Here we study the two-body Sachdev-Ye-Kitaev model and show that the spectral form factor features an exponential ramp, in sharp contrast to the linear ramp in chaotic models. We find a novel mechanism for this exponential ramp in terms of a high-dimensional manifold of saddle points in the path integral formulation of the spectral form factor. This manifold arises because the theory enjoys a large symmetry group. With finite nonintegrable interaction strength, these delicate symmetries reduce to a relative time translation, causing the exponential ramp to give way to a linear ramp.

Perturbed Sachdev-Ye-Kitaev Model: A Polaron in the Hyperbolic Plane

We study the Sachdev-Ye-Kitaev (SYK_{4}) model with a weak SYK_{2} term of magnitude Γ beyond the simplest perturbative limit considered previously. For intermediate values of the perturbation strength, J/N≪Γ≪J/sqrt[N], fluctuations of the Schwarzian mode are suppressed, and the SYK_{4} mean-field solution remains valid beyond the timescale t_{0}∼N/J up to t_{*}∼J/Γ^{2}. The out-of-time-order correlation function displays at short time intervals exponential growth with maximal Lyapunov exponent 2πT, but its prefactor scales as T at low temperatures T≤Γ.

Towards quantum simulation of Sachdev-Ye-Kitaev model

We study a simplified version of the Sachdev-Ye-Kitaev (SYK) model with real interactions by exact diagonalization. Instead of satisfying a continuous Gaussian distribution, the interaction strengths are assumed to be chosen from discrete values with a finite separation. A quantum phase transition from a chaotic state to an integrable state is observed by increasing the discrete separation. Below the critical value, the discrete model can well reproduce various physical quantities of the original SYK model, including the volume law of the ground-state entanglement, level distribution, thermodynamic entropy, and out-of-time-order correlation (OTOC) functions. For systems of size up to N=20, we find that the transition point increases with system size, indicating that a relatively weak randomness of interaction can stabilize the chaotic phase. Our findings significantly relax the stringent conditions for the realization of SYK model, and can reduce the complexity of various experimental proposals down to realistic ranges.

Connecting the SYK Dots

We study a putative (strange) metal-to-insulator transition in a granular array of the Sachdev–Ye–Kitaev (SYK) quantum dots, each occupied by a large number N ≫ 1 of charge-carrying fermions. Extending the previous studies, we complement the SYK couplings by the physically relevant Coulomb interactions and focus on the effects of charge fluctuations, evaluating the conductivity and density of states. The latter were found to demonstrate marked changes of behavior when the effective inter-site tunneling became comparable to the renormalized Coulomb energy, thereby signifying the transition in question.

Quantum Criticality of Granular Sachdev-Ye-Kitaev Matter

We consider granular quantum matter defined by Sachdev-Ye-Kitaev dots coupled via random one-body hopping. Within the framework of Schwarzian field theory, we identify a zero-temperature quantum phase transition between an insulating phase at weak and a metallic phase at strong hopping. The critical hopping strength scales inversely with the number of degrees of freedom on the dots. The increase of temperature out of either phase induces a crossover into a regime of strange metallic behavior.

Sachdev-Ye-Kitaev Model with Quadratic Perturbations: The Route to a Non-Fermi Liquid

We study stability of the Sachdev-Ye-Kitaev (SYK_{4}) model with a large but finite number of fermions N with respect to a perturbation, quadratic in fermionic operators. We develop analytic perturbation theory in the amplitude of the SYK_{2} perturbation and demonstrate stability of the SYK_{4} infrared asymptotic behavior characterized by a Green function G(τ)∝1/τ^{3/2}, with respect to weak perturbation. This result is supported by exact numerical diagonalization. Our results open the way to build a theory of non-Fermi-liquid states of strongly interacting fermions.

Universal Properties of Many-Body Localization Transitions in Quasiperiodic Systems

The precise nature of many-body localization (MBL) transitions in both random and quasiperiodic (QP) systems remains elusive so far. In particular, whether MBL transitions in QP and random systems belong to the same universality class or two distinct ones has not been decisively resolved. Here, we investigate MBL transitions in one-dimensional (d=1) QP systems as well as in random systems by state-of-the-art real-space renormalization group (RG) calculation. Our real-space RG shows that MBL transitions in 1D QP systems are characterized by the critical exponent ν≈2.4, which respects the Harris-Luck bound (ν>1/d) for QP systems. Note that ν≈2.4 for QP systems also satisfies the Harris-Chayes-Chayes-Fisher-Spencer bound (ν>2/d) for random systems, which implies that MBL transitions in 1D QP systems are stable against weak quenched disorder since randomness is Harris irrelevant at the transition. We shall briefly discuss experimental means to measure ν of QP-induced MBL transitions.

Seeking to Develop Global SYK-Ness

Inspired by the recent interest in the Sachdev–Ye–Kitaev (SYK) model, we study a class of multi-flavored one- and two-band fermion systems with no bare dispersion. In contrast to the previous work on the SYK model that would routinely assume spatial locality, thus unequivocally arriving at the so-called ‘locally-critical’ scenario, we seek to attain a spatially-dispersing ‘globally-SYK’ behavior. To that end, a variety of the Lorentz-(non)invariant space-and/or-time dependent algebraically decaying interaction functions is considered and some of the thermodynamic and transport properties of such systems are discussed.

Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model

Quantum chaos is one of the distinctive features of the Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions in 0+1 dimensions with infinite-range two-body interactions, which is attracting a lot of interest as a toy model for holography. Here we show analytically and numerically that a generalized SYK model with an additional one-body infinite-range random interaction, which is a relevant perturbation in the infrared, is still quantum chaotic and retains most of its holographic features for a fixed value of the perturbation and sufficiently high temperature. However, a chaotic-integrable transition, characterized by the vanishing of the Lyapunov exponent and spectral correlations given by Poisson statistics, occurs at a temperature that depends on the strength of the perturbation. We speculate about the gravity dual of this transition.