Transport-Noise Witnesses of Electronic Multipartite Entanglement

How can intrinsic multipartite entanglement among interacting electrons be directly certified in macroscopic solid-state materials, particularly in low-temperature platforms like flat-band two-dimensional systems where conventional spectroscopic probes such as high-resolution neutron or x-ray scattering are inaccessible?

To address this challenge, the authors develop a transport-based protocol that utilizes the equilibrium current-noise spectrum as an experimentally accessible observable. By integrating, symmetrizing, and projecting the current noise, they convert the measured spectrum into the quantum Fisher information (QFI) of the current operator. The method isolates quantum fluctuations from classical thermal (Johnson) noise by applying a hyperbolic tangent frequency kernel. They establish strict upper bounds on the noise QFI for k-producible (separable or partially entangled) states, which serve as a basis-invariant witness. Furthermore, they tighten these bounds by projecting onto active low-energy bands (such as via Schrieffer-Wolff downfolding) and by enforcing point-group symmetries like C3 rotational invariance. The framework is benchmarked across the Hubbard model using determinant quantum Monte Carlo and density-matrix renormalization group, as well as in twisted bilayer graphene and twisted bilayer MoTe2 using exact diagonalization.

Applying the framework to the single-band Hubbard model reveals that symmetrized current-noise spectral weights grow significantly upon cooling, despite the weakening of thermal fluctuations. The calculated noise QFI successfully surpasses the separable-state upper bound below specific temperature and interaction thresholds, thereby certifying at least bipartite entanglement in the Mott insulating regime. In twisted bilayer graphene, active-band projections demonstrate that eigenvalue distributions concentrate near zero as the twist angle approaches the magic angle, substantially lowering the upper bounds for separable states. In twisted bilayer MoTe2, the method certifies topological entanglement in the fractional Chern insulator state at fractional hole fillings. Incorporating C3 rotational symmetry further reduces the upper bounds by roughly 30%, highlighting how crystalline symmetries improve the sensitivity of transport-noise entanglement detection.

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