Accelerated convergence in exact-diagonalization studies

A simple method is proposed and tested for obtaining accelerated convergence of quantum systems on small lattices with N sites. The main idea is to perform exact diagonalizations with some added irrelevant parameter, and use this parameter to accelerate the convergence to the infinite-lattice limit. In this paper different boundary conditions are used to improve the convergence for the Heisenberg model. In particular, we find that the application of the method to the d=1 antiferromagnetic Heisenberg model changes the rate of convergence of the ground-state energy per site, ‖${\mathit{E}}_0$(N)-${\mathit{E}}_0$(∞)‖∼${\mathit{N}}^{\mathrm{-}\mathit{x}}$, to x≊4 from the value x=2, which is found using only periodic boundary conditions.