Generalized lanczos algorithm for variational quantum Monte Carlo - art. no. 024512

We show that the standard Lanczos algorithm can be efficiently implemented statistically and self-consistently improved, using the stochastic reconfig uration method, which has been recently introduced to stabilize the Monte C arlo sign problem instability. With this scheme a few Lanczos steps over a given variational wave function are possible even for large size as a parti cular case of a more general and more accurate technique that allows to obt ain lower variational energies. This method has been tested extensively for a strongly correlated model like the t-J model. With the standard Lanczos technique it is possible to compute any kind of correlation functions, with no particular computational effort. By using the fact that the variance <H -2>-<H > (2) is zero for an exact eigenstate, we show that the approach to the exact solution with few Lonczos iterations is indeed possible even for similar to 100 electrons for reasonably good initial wave functions. The va riational stochastic reconfiguration technique presented here allows in gen eral a many-parameter energy optimization of any computable many-body wave function, including for instance generic long-range Jastrow factors and arb itrary site-dependent orbital determinants. This scheme improves further th e accuracy of the calculation, especially for long-distance correlation fun ctions.