Detecting Topological Transitions and Anisotropy through Multipartite Entanglement in Holographic Weyl Semimetals

Abstract

We study multipartite entanglement structures in the zero-temperature holographic Weyl semimetal, focusing on tripartite and four-partite structures. For strip regions, we compute the conditional mutual information, the entanglement wedge cross section, tripartite measures $\hat{I}º$ and the Markov gap, multi-EWCS, and two multi-EWCS based four-partite signals $\hat{I}”$ and $g$. These quantities are studied as functions of the strip width $l$ and the tuning parameter across the topological transition. At large $l$, their $l$ dependence takes a power-law form governed by the IR scaling of the system. At fixed large $l$, all these entanglement quantities develop clear features near the critical point, showing that tripartite and four-partite entanglement structures can diagnose the topological quantum phase transition. We further study strips pointing in different directions to probe the anisotropy of the system. The anisotropic large l behavior distinguishes the nontrivial phase from the trivial phase. These results establish multipartite holographic entanglement as a sensitive, nonlocal probe of topological phase transitions and anisotropic IR physics.

49 pages, 39 figures, 3 tables