标题： 稀疏SYK模型中的多部分信息 显示英文标题

标题： Multipartite information in sparse SYK models

摘要： 在允许引力对偶的量子场论中，关于任意不相交的空间区域之间的纠缠熵的特定不等式成立。 一个例子是三部分信息的非正性。 受此启发，我们研究了Sachdev-Ye-Kitaev（SYK）和稀疏SYK模型中的类似熵不等式，这些不等式涉及不同风味的马约拉纳费米子之间的纠缠，而不是空间纠缠。 稀疏SYK模型是指其中一些SYK耦合被设为零的模型。 由于这些模型被认为在一定稀疏程度下允许引力对偶，因此有趣的是观察多体纠缠结构是否以依赖于稀疏程度的方式发生变化。 在我们进行数值分析的参数空间中，该分析最多涉及五方，我们发现对于任意温度和稀疏程度以及任意选择的风味子区域，所有熵不等式都得到满足。 此外，如果我们以纯度为基准绘制多体纠缠熵，稀疏程度的唯一显著影响是改变纯度的范围。 因此，我们得出结论，多体信息几乎不受稀疏程度的影响。 作为反例，我们还展示了在包含没有随机变量的$N$-风味马约拉纳费米子的矢量模型中，存在某些子区域的选择，使得熵不等式被违反。 显示英文摘要

摘要： In quantum field theories that admit gravity dual, specific inequalities involving entanglement entropy between arbitrary disjoint spatial regions hold. An example is the negativity of tripartite information. Inspired by this, we investigate the analogous entropy inequalities in Sachdev-Ye-Kitaev (SYK) and sparse SYK models, which involve the entanglement among different flavors of Majorana fermions rather than spatial entanglement. Sparse SYK models are models where some of the SYK couplings are set to zero. Since these models have been argued to admit gravity duals up to a certain sparseness, it is interesting to see whether the multipartite entanglement structure changes in a sparseness-dependent manner. In the parameter space explored by our numerical analysis, which we performed upto five parties, we find that all entropy inequalities are satisfied for any temperature and degree of sparseness for an arbitrary choice of flavor subregions. In addition, if we plot the multipartite entanglement entropy in terms of purity, the only significant effect of sparseness is to change the range of purity. Thus, we conclude that multipartite information is almost unaffected by sparseness. As a counterexample, we also show that in a vector model of $N$-flavored Majorana fermions which contains no random variables, choices of subregions exist for which the entropy inequalities are violated.