Characterization of Exciton-exciton entanglement in different phases: A many-body investigation in low dimensions

There have been emerging experimental investigations on exciton-exciton correlations, especially in moiré superlattices [1]. However, theoretical understanding of exciton–exciton interactions - which requires an accurate treatment of four-point Green’s functions and the validity of a bosonic description of excitons- remains relatively underdeveloped. We construct an exactly solvable one-dimensional model to investigate exciton–exciton correlations and entanglement using many-body exact techniques. We identify phase boundaries separating excitonic phases with different degrees of binding, and extrapolate the data to the thermodynamic limit to infer properties in large systems.

We also apply a wavefunction projection technique to characterize the strength of entanglement between excitons, as well as the strength of entanglement between the electron and hole inside an exciton. Our results show that, over a broad parameter range, excitonic correlations remain weak, validating the applicability of many-body perturbation theory in most cases. We also explored the quantum confinement effect of multi-exciton state in 1D systems and uncovered the conditions under which the confinement effects emerge.

[1] R. Xiong, J. H. Nie, S. L. Brantly, P. Hays, R. Sailus, K. Watanabe, T. Taniguchi, S. Tongay, and C. Jin. Science 380, 860 (2023).