Multipartite entanglement characterizing topological phase transitions in holographic nodal line semimetals

TL;DR

This paper explores how multipartite entanglement measures can serve as sensitive indicators of topological phase transitions in strongly coupled holographic nodal line semimetals, revealing non-local order parameters that detect critical points.

Contribution

It introduces the use of multipartite entanglement measures as probes for topological phase transitions in holographic semimetals, highlighting their sensitivity to topology and criticality.

Findings

Multipartite measures vanish at large distances, confirming short-range entanglement.

Large-distance scaling behavior is highly sensitive to the system's topology.

Power-law decay exponents act as non-local order parameters at quantum critical points.

Abstract

Topological states of matter are characterized by nonlocal structures that are naturally encoded in the quantum entanglement of many-body wavefunctions. Topological semimetals are short-range entangled states at weak coupling and their entanglement structure at strong coupling remains largely unexplored. In this work, we investigate the multipartite entanglement structure of strongly coupled holographic nodal line semimetals. Building on previous studies of entanglement entropy and the holographic c-function, we focus on multipartite entanglement measures, including the conditional mutual information, multi-entropy, and the Markov gap which is based on the entanglement wedge cross section. Our results demonstrate that while these multipartite measures vanish in the long-distance limit $l \to \infty$, which confirms that the holographic nodal line semimetal remains a short-range entangled state, their large $l$ scaling behavior remains highly sensitive to the underlying topology. The large $l$ power-law decay and scaling exponents serve as robust, non-local order parameters that exhibit sharp changes at the quantum critical point. This work establishes multi-partite entanglement as a powerful probe of quantum topological phase transitions in strongly coupled topological systems.