Beyond the quasiparticle approximation: Fully self-consistent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>G</mml:mi><mml:mi>W</mml:mi></mml:mrow></mml:math> calculations

The $G\phantom{\rule{0}{0ex}}W$ method of Lars Hedin is the most popular approach to predict electron addition and removal energies in solids. To date, most $G\phantom{\rule{0}{0ex}}W$ calculations are performed assuming that the many-body system features sharp resonances, also known as quasiparticle peaks. The authors go beyond this approximation and determine the Green's function $G$ and the screened interaction $W$ fully self-consistently in the $G\phantom{\rule{0}{0ex}}W$ approximation. They find strong broadening of the quasiparticle peaks. Somewhat disappointingly, the predicted band gaps are too large. This notwithstanding, the work is an important step towards a full solution of Hedin's equations.