Excited state calculations in solids by auxiliary-field quantum Monte Carlo

We have studied electronic excitations in solid systems using the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method.\footnote{S.~Zhang and H.~Krakauer, Phys.~Rev.~Lett.~{\bf 90}, 136401 (2003); W.~Purwanto, S.~Zhang, and H.~Krakauer, J. Chem. Phys. {\bf 130}, 094107 (2009).} Trial wave functions for excited states are simply constructed from the corresponding density functional theory (DFT) ground state orbitals by promoting electrons to conduction bands. The post-processing finite size (FS) correction method\footnote{F.~Ma, S.~Zhang, and H.~Krakauer, Phys.~Rev.~B {\bf 84}, 155130 (2011); H.~Kwee, S.~Zhang, and H.~Krakauer, Phys. Rev. Lett. {\bf 100}, 126404 (2008).} is applied to remove the many-body FS effects. By fitting the calculated excitation energies at various crystal momentum values, a many-body electronic band structure is obtained. Our results for prototypical semiconductors such as silicon are compared to those from the GW approximation\footnote{M.~Rohlfing, P.~Kr\"uger, and J.~Pollmann, Phys.~Rev B.~{\bf 48}, 17791 (1993).} and diffusion Monte Carlo calculations.\footnote{A.~J.~Williamson, R.~Q.~Hood, R.~J.~Needs, and G.~Rajagopal, Phys.~Rev.~B {\bf 57}, 12140 (1998).}