Autoregressive neural Slater-Jastrow ansatz for variational Monte Carlo simulation

Direct sampling from a Slater determinant is combined with an autoregressive deep neural network

as a Jastrow factor into a fully autoregressive Slater-Jastrow ansatz for variational quantum Monte

Carlo, which allows for uncorrelated sampling. The elimination of the autocorrelation time leads

to a stochastic algorithm with provable cubic scaling (with a potentially large prefactor), i.e. the

number of operations for producing an uncorrelated sample and for calculating the local energy

scales like O(N_s³) with the number of orbitals (lattice sites) N_s , largely independent of the filling. In

cases where the autocorrelation time scales with the system size this drastically changes the scaling

of the computational effort for achieving a certain Monte Carlo error. Direct sampling also improves

the sampling efficiency compared to the Metropolis update which can suffer from bottlenecks due

to low acceptance rate. The implementation is benchmarked on the two-dimensional t − V model of

spinless fermions on the square lattice by comparison with exact diagonalization, yielding consistent

results for a variational ansatz which is limited by the sign structure of a single Slater determinant.

By co-optimizing the reference Slater determinant in the presence of the Jastrow factor the sign

structure of the initial Hartree-Fock Slater determinant can be changed considerably, which aids the

optimization.