  The existence of polyexcitons, the $N$-body complexes of excitons for $N > 2$
in 3D bulk systems, has been controversial for more than 40 years since its
first theoretical suggestion. We investigated the stability of fundamental
excitonic complexes in diamond numerically with the stochastic variational
method (SVM) and an explicitly correlated Gaussian (ECG) basis. The
electron-hole many-body system is described by an effective mass Hamiltonian.
Our model includes the effective mass anisotropy and multiple valley and band
degrees of freedom. We show that the excitons, trions, biexcitons, charged
biexcitons, and triexcitons are stable in diamond. Numerical calculations
reproduce from 81% to 86% of the experimentally reported binding energies for
neutral bound states.
