Anderson Misobuchi

We use a combination of analytical and numerical methods to study out-of-time order correlators (OTOCs) in the sparse Sachdev-Ye-Kitaev (SYK) model. We find that at a given order of N , the standard result for the q-local, all-to-all SYK, obtained through the sum over ladder diagrams, is corrected by a series in the sparsity parameter, k. We present an algorithm to sum the diagrams at any given order of 1/(kq)n. We also study OTOCs numerically as a function of the sparsity parameter and determine the Lyapunov exponent. We find that numerical stability when extracting the Lyapunov exponent requires averaging over a massive number of realizations. This trade-off between the efficiency of the sparse model and consistent behavior at finite N becomes more significant for larger values of N .

We use a combination of analytical and numerical methods to study out-of-time order correlators (OTOCs) in the sparse Sachdev-Ye-Kitaev (SYK) model. We find that at a given order of N, the standard result for the q-local, all-to-all SYK, obtained through the sum over ladder diagrams, is corrected by a series in the sparsity parameter, k. We present an algorithm to sum the diagrams at any given order of 1/(kq)ⁿ. We also study OTOCs numerically as a function of the sparsity parameter and determine the Lyapunov exponent. We find that numerical stability when extracting the Lyapunov exponent requires averaging over a massive number of realizations. This trade-off between the efficiency of the sparse model and consistent behavior at finite N becomes more significant for larger values of N.

We investigate the spectral form factor of the sparse Sachdev-Ye-Kitaev model. We use numerical methods to establish that at intermediate times the connected part of the spectral form factor is the dominant one. These connected contributions arise from fluctuations around the disconnected geometry, not from a new saddle point. A similar effect was previously conjectured in SYK but required a value of N out of reach of current numerical simulations.

We investigate two sparse Sachdev-Ye-Kitaev (SYK) systems coupled by a bilinear term as a holographic quantum mechanical description of an eternal traversable wormhole in the low temperature limit. Each SYK system consists of N Majorana fermions coupled by random q-body interactions. The degree of sparseness is captured by a regular hypergraph in such a way that the Hamiltonian contains exactly k N independent terms. We improve on the theoretical understanding of the sparseness property by using known measures of hypergraph expansion. We show that the sparse version of the two coupled SYK model is gapped with a ground state close to a thermofield double state. Using Krylov subspace and parallelization techniques, we simulate the system for q = 4 and q = 8. The sparsity of the model allows us to explore larger values of N than the ones existing in the literature for the all-to-all SYK. We analyze in detail the two-point functions and the transmission amplitude of signals between the two systems. We identify a range of parameters where revivals obey the scaling predicted by holography and signals can be interpreted as traversing the wormhole.

In higher derivative theories, gravity can travel slower or faster than light. With this feature in mind, we revisit the construction of the causal and entanglement wedges in this type of theories, and argue that they must be constructed using the fastest mode instead of null rays. We show that the property of causal wedge inclusion, i.e., the fact that the causal wedge must be contained in the entanglement wedge, leads to more stringent constraints on the couplings than those imposed by hyperbolicity and boundary causality. Our results imply that the full power of subregion-subregion duality could lead to the same conclusions previously obtained based on high energy graviton scattering. We illustrate our findings with a systematic analysis in Gauss-Bonnet gravity.

In higher derivative theories, gravity can travel slower or faster than light. With this feature in mind, we revisit the construction of the causal and entanglement wedges in this type of theories, and argue that they must be constructed using the fastest mode instead of null rays. We show that the property of causal wedge inclusion, i.e., the fact that the causal wedge must be contained in the entanglement wedge, leads to more stringent constraints on the couplings than those imposed by hyperbolicity and boundary causality. Our results imply that the full power of subregion-subregion duality could lead to the same conclusions previously obtained based on high energy graviton scattering. We illustrate our findings with a systematic analysis in Gauss-Bonnet gravity.

In this work we explore the effect of rotation in the size of a traversable wormhole obtained via a double trace boundary deformation. We find that at fixed temperature the size of the wormhole increases with the angular momentum J/M ℓ. The amount of information that can be sent through the wormhole increases as well. However, for the type of interaction considered, the wormhole closes as the temperature approaches the extremal limit. We also briefly consider the scenario where the boundary coupling is not spatially homogeneous and show how this is reflected in the wormhole opening.