Genuine $k$-partite correlations and entanglement in the ground state of the Dicke model for interacting qubits

TL;DR

This paper investigates genuine multipartite correlations and entanglement in the ground state of the Dicke model with interacting qubits, revealing their role in quantum phase transitions and potential experimental realizations.

Contribution

It introduces a method to quantify genuine multipartite correlations in the Dicke model, including their behavior across phase transitions and connection to entanglement detection.

Findings

GMC signals both first- and second-order quantum phase transitions.

GMC encompasses classical and quantum correlations.

QFI used to detect genuine multipartite entanglement.

Abstract

Here, we calculate and study correlations of the Dicke model in the presence of qubit-qubit interaction. Whereas the analysis of correlations among its subsystems is essential for the understanding of corresponding critical phenomena and for performing quantum information tasks, the majority of correlation measures are restricted to bipartitions due to the inherent challenges associated with handling multiple partitions. To circunvent this we employ the calculation of Genuine Multipartite Correlations (GMC) based on the invariance of our model under particle permutation. We then quantify the correlations within each subpart of the system, as well as the percentage contribution of each GMC of order $k$, highlighting the many-body behaviors for different regimes of parameters. Additionally, we show that GMC signal both first- and second-order quantum phase transitions present in the model. Furthermore, as GMC encompasses both classical and quantum correlations, we employ Quantum Fisher Information (QFI) to detect genuine multipartite entanglement. Ultimately, we map the Dicke model with interacting qubits to spin in solids interacting with a quantum field of magnons, thus demonstrating a potential experimental realization of this model.