Phaseless auxiliary-field quantum Monte Carlo method for cavity-QED matter systems

We present a generalization of the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method to cavity

quantum-electrodynamical (QED) matter systems. The method can be formulated in both the Coulomb and

the dipole gauge. We verify its accuracy by benchmarking calculations on a set of small molecules against full

configuration interaction and state-of-the-art QED coupled cluster (QED-CCSD) calculations. Our results

show that (i) gauge invariance can be achieved within correlation-consistent Gaussian basis sets, (ii) the

accuracy of QED-CCSD can be enhanced significantly by adding the standard perturbative triples correction

without light-matter coupling, and (iii) there is a straightforward way to evaluate the differential expression

for the photon occupation number that works in any gauge. The high accuracy and favorable computational

scaling of our AFQMC approach will enable a broad range of applications. Besides polaritonic chemistry, the

method opens a way to simulate extended QED matter systems.