We study a sparse version of the Sachdev-Ye-Kitaev (SYK) model defined on random hypergraphs constructed either by a random pruning procedure or by randomly sampling regular hypergraphs. The resulting model has a new parameter, $k$, defined as the ratio of the number of terms in the Hamiltonian to the number of degrees of freedom, with the sparse limit corresponding to the thermodynamic limit at fixed $k$. We argue that this sparse SYK model recovers the interesting global physics of ordinary SYK even when $k$ is of order unity. In particular, at low temperature the model exhibits a gravitational sector which is maximally chaotic. Our argument proceeds by constructing a path integral for the sparse model which reproduces the conventional SYK path integral plus gapped fluctuations. The sparsity of the model permits larger scale numerical calculations than previously possible, the results of which are consistent with the path integral analysis. Additionally, we show that the sparsity of the model considerably reduces the cost of quantum simulation algorithms. This makes the sparse SYK model the most efficient currently known route to simulate a holographic model of quantum gravity. We also define and study a sparse supersymmetric SYK model, with similar conclusions to the non-supersymmetric case. Looking forward, we argue that the class of models considered here constitute an interesting and relatively unexplored sparse frontier in quantum many-body physics.
The sparse version of the Sachdev-Ye-Kitaev (SYK) model reproduces essential features of the original SYK model while reducing the number of disorder parameters. In this paper, we propose a further simplification of the model which we call the binary-coupling sparse SYK model. We set the nonzero couplings to be $\pm 1$, rather than being sampled from a continuous distribution such as Gaussian. Remarkably, this simplification turns out to be an improvement: the binary-coupling model exhibits strong correlations in the spectrum, which is the important feature of the original SYK model that leads…
We study the error threshold properties of holographic quantum error-correcting codes. We demonstrate that holographic CFTs admit an algebraic threshold, which is related to the confinement-deconfinement phase transition. We then apply geometric intuition from holography and the Hawking-Page phase transition to motivate the CFT result, and comment on potential extensions to other confining theories.
We calculate the transport of a theory with two conserved currents by holographic method and compare it with graphene data to determine its dynamical exponents $(z,θ)$ which characterizes a QCP. As a result, we find that the electric and the thermal conductivity data can be fit much more naturally if we assume $(z,θ)=(3/2,1)$ rather than $(1,0)$. Furthermore, we find that thermoelectric power data at high temperature can be fit if we use $(3/2,1)$ but not at all by $(1,0)$. The $θ=1$ result can be interpreted as taking into account the fermionic nature of the electrons and $z=3/2$ can be inter…
We investigate aspects of non-equilibrium dynamics of strongly coupled field theories within holography. We establish a hydrodynamic description for anomalous quantum field theories subject to a strong external field for the first time in the literature. Within holography, we explicitly demonstrate which transport coefficients are non-zero due to the chiral anomaly and thus important for the transport. We show that the standard treatment of the hydrodynamics for spontaneously broken translational invariance is more subtle and has to be revised since the description is missing a novel thermodyn…
