Abstract The Sachdev-Ye-Kitaev (SYK) model incorporates rich physics, ranging from exotic non-Fermi liquid states without quasiparticle excitations, to holographic duality and quantum chaos. However, its experimental realization remains a daunting challenge due to various unnatural ingredients of the SYK Hamiltonian such as its strong randomness and fully nonlocal fermion interaction. At present, constructing such a nonlocal Hamiltonian and exploring its dynamics is best through digital quantum simulation, where state-of-the-art techniques can already handle a moderate number of qubits. Here, we demonstrate a first step towards simulation of the SYK model on a nuclear-spin-chain simulator. We observed the fermion paring instability of the non-Fermi liquid state and the chaotic-nonchaotic transition at simulated temperatures, as was predicted by previous theories. As the realization of the SYK model in practice, our experiment opens a new avenue towards investigating the key features of non-Fermi liquid states, as well as the quantum chaotic systems and the AdS/CFT duality.
We propose a low energy model for simulating an analog black hole on an optical lattice using ultracold atoms. Assuming the validity of the holographic principle, we employ the Sachdev-Ye-Kitaev (SYK) model, which describes a system of randomly infinite range interacting fermions, also conjectured to be an exactly solvable UV-complete model for an extremal black hole in a higher dimensional Anti-de Sitter (AdS) dilaton gravity. At low energies, the SYK model exhibits an emergent conformal symmetry and is dual to the extremal black hole solution in near AdS2 spacetime. Furthermore, we show how the SYK maximally chaotic behaviour at large N limit, found to be dual to a gauge theory in higher dimensions, can also be employed as a non-trivial investigation tool for the holographic principle. The proposed setup is a theoretical platform to realize the SYK model with relevant exotic effects and behaviour at low energies as a highly non-trivial example of the AdS/CFT duality and a framework for studying black holes.
The Sachdev-Ye-Kitaev (SYK) model is a concrete model for a non-Fermi liquid with maximally chaotic behavior in
(0+1) dimensions. In order to gain some insights into real materials in higher dimensions where fermions could hop between different sites, here we consider coupling a SYK lattice by constant hopping. We call this the dispersive SYK model. Focusing on
(1+1)-dimensional homogeneous hopping, by either tuning the temperature or the relative strength of the random interaction (hopping) and constant hopping, we find a crossover between a dispersive metal to an incoherent metal, where the dynamic exponent
z changes from 1 to $\ensuremath{\infty}$. We study the crossover by calculating the spectral function, charge density correlator, and the Lyapunov exponent. We further find the Lyapunov exponent becomes larger when the chemical potential is tuned to approach a van Hove singularity because of the large density of states near the Fermi surface. The effect of the topological nontrivial bands is also discussed.
We suggest that the holographic principle, combined with recent technological advances in atomic, molecular, and optical physics, can lead to experimental studies of quantum gravity. As a specific example, we consider the Sachdev–Ye–Kitaev (SYK) model, which consists of spin-polarized fermions with an all-to-all complex random two-body hopping and has been conjectured to be dual to a certain quantum-gravitational system. Achieving low-temperature states of the SYK model is interpreted as a realization of a stringy black hole, provided that the holographic duality is true. We introduce a variant of the SYK model, in which the random two-body hopping is real. This model is equivalent to the original SYK model in the large-|
N| limit. We show that this model can be created in principle by confining ultracold fermionic atoms into optical lattices and coupling two atoms with molecular states via photo-association lasers. This development serves as an important first step towards an experimental realization of such systems dual to quantum black holes. We also show how to measure out-of-time-order correlation functions of the SYK model, which allow for identifying the maximally chaotic property of the black hole.
The complex Sachdev-Ye-Kitaev (SYK) model, featuring fermions with all-to-all interactions, serves as a dual paradigm for understanding non-Fermi liquid behavior and the holographic nature of charged black holes. Two defining characteristics of the standard SYK model are its maximal chaos (Lyapunov exponent
λL=2πT at temperature
T), and its finite zero-temperature residual entropy. While previous studies have largely focused on couplings drawn from a zero-mean Gaussian distribution, we investigate a generalized model with a finite mean-to-standard-deviation ratio,
g≡J0/δJ of the coupling distribution in order to get deeper insight into the evolution of chaos. We find that increasing
g yields the following effects: (i) The system remains a fast scrambler with
λL=A T, but with a suppressed coefficient
A<2π. (ii) In the limit
g→∞, out-of-time-ordered correlators (OTOCs) no longer exhibit exponential growth with
λL≃0. (iii) The spectral correlations indicative of late-time chaos maintain Wigner-Dyson level spacing statistics for all values of
g. (iv) The system preserves a finite residual entropy, albeit with reduced magnitude, for all
g values. We conclude that in this generalized SYK model, there is a chaotic to non-chaotic crossover. Moreover different measures of chaos decouple, demonstrating that the presence of finite residual entropy does not strictly imply maximal chaos.
The Sachdev--Ye--Kitaev (SYK) model is a paradigm for extreme quantum chaos, non-Fermi-liquid behavior, and holographic matter. Yet, the dense random all-to-all interactions that characterize it are an extreme challenge for realistic laboratory realizations. Here, we propose a general scheme for densifying the coupling distribution of random disorder Hamiltonians, using a Trotterized cycling through sparse time-dependent disorder realizations. To diagnose the convergence of sparse to dense models, we introduce an information-theory inspired diagnostic. We illustrate how the scheme can come to bear in the realization of the complex SYK
4 model in cQED platforms with available experimental resources, using a single cavity mode together with a fast cycling through independent speckle patterns. The simulation scheme applies to the SYK class of models as well as spin glasses, spin liquids, and related disorder models, bringing them into reach of quantum simulation using single-mode cavity-QED setups and other platforms.