Characterization of Exciton-exciton entanglement and correlations

Abstract

Excitons in the weakly interacting regime can be well-described by many-body perturbation theories such as the Bethe-Salpeter equation formalism. However, for materials such as transition metal dichalcogenides moiré heterostructures under strong illumination, with the emergence of dense excitonic states, the strong correlation and entanglement between electrons and holes may cause the many-body perturbation method to fail, and excitons may not be treated in the bosonic picture, but exhibit fermionic behaviors. In our work, we investigate the phase space where excitons, and the electrons and holes which constitute them, are weakly or strongly entangled, as well as their binding for different interaction profiles and the degree of localization of the electrons and holes. We corroborate the validity of using many-body perturbation theory in the exciton with interactions. Our work provides a general way to analyze the correlation and entanglement of multi-particle excitations in many-body systems, and gives a more comprehensive understanding of different phases for exciton entanglement and interactions in 1D systems.

Figures (3)

• Figure 1: (a) Our 1D model to investigate exciton-exciton interactions. (b-d) Exponential decay of the attractive and repulsive interactions. (b) A case where the repulsive interaction dominates at all distances. (c) A case where the repulsive interaction dominates at shorter distances, but the attractive interaction dominates at longer distances. (d) A case where the attractive interaction dominates at shorter distances, but the repulsive interaction dominates at longer distances. The quantum confinement of multiexcitations occurs in this case.
• Figure 2: Calculated phase boundaries and extrapolation of the thermodynamic limit of phase transitions. (a) Schematic diagram for double excitation states when they are characterized in e-h plasma, bound e-h, or strongly bound phase. The purple dashed arrows denote the binding between particles, and the blue and red wavy lines denote the entanglement. (b) When $\frac{\gamma_U}{\gamma_V} = 1.0, \frac{U^0}{V^0} = 2.8$, it is in the boundary of an LA model and a PR model, corresponding to the purple linecut in Fig. \ref{['fig:4']}(b). In this case, both the boundary to enter SB and EG are monotonously increasing as $N_{site}$ goes larger, so there is no quantum confinement effect. (c)When $\frac{\gamma_U}{\gamma_V} =2.0$, $\frac{U^0}{V^0} = 0.8$, it is an SA model, corresponding to the purple linecut in Fig. \ref{['fig:4']}(a). It shows the quantum confinement effect for multi-excitations.
• Figure 3: Phase diagrams in the thermodynamic limit representing transitions between different cases. (a) Phase diagram for fixed $U^0/V^0 = 0.8$ and changing $\gamma_U/\gamma_V$, the system goes from SA models to nearly PR models. The quantum confinement happens when $\sim 1.9 < \gamma_U/\gamma_V < \sim 2.8$, where the model is SA. At large $\gamma_U/\gamma_V$, both the phase boundary between SB and EG and the phase boundary between EG and e-h plasma exhibit quadratic behavior. The purple line corresponds to the case shown in Fig.\ref{['fig:2']}(c). (b) Phase diagram for fixed $U^0/V^0 = 2.8$, and changing $\gamma_U/\gamma_V$, the system goes from LA models to PR models. The system has strongly correlated exciton phases when $\gamma_U/\gamma_V < \sim 1.0$ where the model is LA. The purple line corresponds to the case shown in Fig.\ref{['fig:2']}(b). (c) Phase diagram for fixed $\gamma_U/\gamma_V = 2.0$, and changing $U^0/V^0$, the system goes from SA models to PR models. The system has quantum confinements when $U^0/V^0 \sim 1.0$ where the model is SA. At large $U^0/V^0$, both the phase boundary between SB and EG and the phase boundary between EG and e-h are nearly constant.