Neutral band gap of Carbon by Quantum Monte Carlo methods

We present a method to calculate the energy gap of a charge-neutral excitation using only ground-state calculations. We report Quantum Monte Carlo calculations of $\Gamma\rightarrow\Gamma$ and $\Gamma\rightarrow X$ particle-hole excitation energies in diamond carbon. We analyze the finite-size effect and find the same $1/L$ decay rate as that in a charged excitation, where L is the linear extension of the supercell. This slow decay is attributed to the delocalized nature of the excitation in supercells too small to accommodate excitonic binding effects. At larger system sizes the apparent $1/L$ decay crosses over to a $1/L^3$ behavior. Estimating the scale of exciton binding can be used to correct finite-size effects of neutral gaps.