Multipartite information in sparse SYK models

TL;DR

This paper investigates multipartite entanglement inequalities in sparse SYK models, finding that sparseness has minimal impact on these inequalities, unlike in a non-random vector model where violations occur.

Contribution

It demonstrates that multipartite entanglement inequalities hold in sparse SYK models across various parameters, showing sparseness does not significantly alter entanglement structure.

Findings

All entropy inequalities satisfied in sparse SYK models across parameters.

Sparseness mainly affects the range of multipartite entropy in terms of purity.

Violations of inequalities occur in a non-random vector model, not in sparse SYK.

Abstract

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.