Multipartite entanglement characterizing topological phase transitions in holographic nodal line semimetals

TL;DR

This work investigates multipartite entanglement in strongly coupled holographic nodal line semimetals as a diagnostic of quantum topological phase transitions. By combining three classes of measures—the conditional mutual information, a genuine tripartite quantity kappa based on the holographic multi-entropy, and multipartite correlations from the entanglement wedge cross section via the Markov gap—the authors show that all tripartite observables vanish at large separation, confirming short-range entanglement, while their large-$l$ scaling exponents encode the infrared topology and exhibit sharp changes at the critical point. The analysis reveals strong anisotropy in entanglement: long-range correlations are suppressed along the nodal-plane directions but enhanced along the out-of-plane direction, all captured by direction-dependent power laws governed by IR scaling exponents $\mathbf{z}$. These results establish multipartite entanglement as robust nonlocal order parameters for holographic topological phase transitions, with potential extensions to other holographic topological semimetals and dynamical quenches.

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.

Figures (15)

• Figure 1: Left: The profile of $f(r)$ for different values of $M/b$. Right: The profile of $\phi(r)$ for different values of $M/b$. The profile for critical phase is shown in black, corresponding $M/b$ is 0.8597.
• Figure 2: Illustration of an extremal surface anchored to a boundary strip along the $x^i$-direction. The surface is constructed by first choosing a turning point $r_*$ deep in the bulk; its corresponding boundary width $l_i$ is then derived from Eq. \ref{['StripWidth']}.
• Figure 3: Left: The evolution of the holographic c-function $c_x$ with $l_x$ for different phases. Right: The evolution of the holographic c-function $c_z$ with $l_z$ for different phases.
• Figure 4: Left: the evolution for $c_x$ with increasing $M/b$. Right: the evolution for $c_z$ with increasing $M/b$.
• Figure 5: Left: The dependence of the values of CMI $I(A:B|E)$ on $l_x$ (left) and $l_z$ (right) for different phases with representative values of $M/b$ in each phase.