Quasiparticle bands in a two-dimensional crystal found byGWand quantum Monte Carlo calculations

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Abstract
A computational investigation of excited states in a model two-dimensional (2D) semiconducting system is presented. We employ three different methods to deal with exchange and correlation effects: a standard band-structure calculation within the local-density approximation (LDA), a quantum Monte Carlo calculation (QMC), and a perturbative calculation within the so-called GW framework. The results confirm that as in three-dimensional systems, the LDA seriously underestimates the band gap. The quantitative agreement between QMC and GW is very good, thus providing evidence that GW calculations may serve as a reliable tool for the investigation of insulating nonmagnetic 2D systems. We also demonstrate numerically that attempts to extract an ‘‘exact’’ exchange-correlation potential from QMC calculations suffer from the insensitivity of the charge density to rapid spatial variations in the mean-field potential.