Title: Neutral band gap of carbon by quantum Monte Carlo methods
Author(s):

	V. Gorelov (LSI, CNRS, CEA/DRF/IRAMIS, É cole Polytechnique, Institut Polytechnique de Paris, F-91120 Palaiseau, France; European Theoretical Spectroscopy Facility (ETSF))
	Y. Yang (Center for Computational Quantum Physics, Flatiron Institute, New York, NY, 10010, USA),
	M. Ruggeri (Maison de la Simulation, CEA, CNRS, Univ. Paris-Sud, UVSQ, Université Paris-Saclay, 91191 Gif-sur-Yvette, France)
	D. M. Ceperley (Department of Physics, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA),
	C. Pierleoni (Department of Physical and Chemical Sciences, University of L'Aquila, Via Vetoio 10, I-67010 L'Aquila, Italy),
	M. Holzmann (Univ. Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France)

We present a method of calculating the energy gap of a charge-neutral excitation using only ground-state calculations. We report Quantum Monte Carlo calculations of Γ→ Γ and Γ → 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/L³ behavior. Estimation of the scale of exciton binding can be used to correct finite-size effects of neutral gaps.

Key words: quantum Monte Carlo, first-principles calculations, electronic structure, excitons, band gap, diamond

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