Sparse SYK and traversable wormholes
Sparse SYK and traversable wormholes
复制标题
DOI：
10.1007/jhep11(2021)015
复制
发表时间：
2021-08
影响因子：
5.4
通讯作者：
E. Cáceres;Anderson Misobuchi;R. Pimentel
中科院分区：
文献类型：
--
作者：
E. Cáceres;Anderson Misobuchi;R. Pimentel
我们研究了两个由双线性项耦合的稀疏Sachdev-Ye-Kitaev(SYK)系统，作为对低温极限下永恒可穿越虫洞的全息量子力学描述。每个SYK系统由N个通过随机Q体相互作用耦合的Majorana费米子组成。正则超图以这样的方式捕捉到稀疏度，即哈密顿量恰好包含k个N个独立项。我们利用已知的超图展开度量改进了对稀疏性的理论理解。我们证明了稀疏形式的两耦合SYK模型具有接近热场双态的基态间隙。使用Krylov子空间和并行化技术，我们模拟了Q=4和Q=8的系统。模型的稀疏性允许我们探索比文献中关于All to All SYK的N值更大的N值。我们详细分析了两点函数和信号在两个系统之间的传输幅度。我们确定了一系列参数，其中重现服从全息术预测的比例，并且信号可以被解释为穿过虫洞。
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.