S. Sorella

Collaborators: M. Calandra F. Becca L. Capriotti and A. Trumper

GFMCSR: an effective remedy for the sign problem disease.


The ''Stochastic Reconfiguration'' scheme for the stabilization of the sign problem in the Green Function Monte Carlo technique (GFMC) is discussed. This method stabilizes the average sign of the walkers during a GFMC simulation by introducing a systematic ''bias'' that can be reduced and eventually vanishes in a well defined theoretical limit. This is achieved when all the independent correlation functions characterizing the Hilbert space of a strongly correlated system are set to be statistically equal before and after the ``Stochastic Reconfiguration''. This exact limit is prohibitive for a physically large Hilbert space, However a considerable reduction of the mentioned ''bias'' can be easily achieved, by considering only few correlation functions in the ''Stochastic Reconfiguration''. The method is applied and tested for three lattice hamiltonians, which still represents a challenge in computational physics due to the ''sign problem'':
  1. the frustrated hard core bosons,
  2. the antiferromagnetic Heisenberg model with frustration,
  3. the t-J model: i.e. the strongly correlated electrons in a lattice.
It will be shown that for all three models the accuracy of the ground state energy per site and of some correlation functions is physically acceptable even for large number of lattice sites and electrons. This property allows us to draw some interesting physical conclusions about the ground state properties of the considered models.

NATO ASI, Cornell Theory Center,

Last modified: Thu Jul 2 10:26:13 EDT 1998