Bipartite Fluctuations and Topology of Dirac and Weyl Systems

TL;DR

This paper explores how bipartite fluctuations reveal topological features in Dirac and Weyl systems, linking charge fluctuations to winding numbers and entanglement properties, especially in non-conserving particle number scenarios.

Contribution

It establishes a connection between bipartite fluctuations, topology, and entanglement in Dirac and Weyl quantum systems, including the role of gap anisotropy and higher dimensions.

Findings

Charge fluctuations relate to winding numbers of Dirac cones.

Topological Hamiltonian features induce long-range entanglement.

Analysis includes effects of gap anisotropy and Weyl analogues.

Abstract

Bipartite fluctuations can provide interesting information about entanglement properties and correlations in many-body quantum systems. We address such fluctuations in relation with the topology of Dirac and Weyl quantum systems, in situations where the relevant particle number is not conserved, leading to additional volume laws scaling with the Quantum Fisher information. Through the example of the $p+ip$ superconductor, we build a relation between charge fluctuations and the associated winding numbers of Dirac cones in the low-energy sector. Topological aspects of the Hamiltonian in the vicinity of these points induce long-range entanglement in real space. We provide a detailed analysis of such fluctuation properties, including the role of gap anisotropy, and discuss higher-dimensional Weyl analogues.