  We develop a local correlation variant of auxiliary field quantum Monte Carlo
(AFQMC) that is based on local natural orbitals (LNO-AFQMC). In LNO-AFQMC,
independent AFQMC calculations are performed for each localized occupied
orbital using a truncated set of tailored orbitals. Because the size of this
space does not grow with system size for a target accuracy, the method has
linear scaling. Applying LNO AFQMC to molecular problems containing a few
hundred to a thousand orbitals, we demonstrate convergence of total energies
with significantly reduced costs. The savings are more significant for larger
systems and larger basis sets. However, even for our smallest system studied,
we find that LNO-AFQMC is cheaper than canonical AFQMC, in contrast with many
other reduced-scaling methods. Perhaps most significantly, we show that energy
differences converge much more quickly than total energies, making the method
ideal for applications in chemistry and material science. Our work paves the
way for linear scaling AFQMC calculations of strongly correlated systems, which
would have a transformative effect on ab initio quantum chemistry.
