  We show that the recently developed phaseless auxiliary-field quantum Monte
Carlo (AFQMC) method can be used to study excited states, providing an
alternative to standard quantum chemistry methods. The phaseless AFQMC
approach, whose computational cost scales as M^3-M^4 with system size M, has
been shown to be among the most accurate many-body methods in ground state
calculations. For excited states, prevention of collapse into the ground state
and control of the Fermion sign/phase problem are accomplished by the
approximate phaseless constraint with a trial wave function. Using the
challenging C2 molecule as a test case, we calculate the potential energy
curves of the ground and two low-lying singlet excited states. The trial wave
function is obtained by truncating complete active space wave functions, with
no further optimization. The phaseless AFQMC results using a small basis set
are in good agreement with exact full configuration interaction calculations,
while those using large basis sets are in good agreement with experimental
spectroscopic constants.
