Control of the finite size corrections in exact diagonalization studies

TL;DR

This paper demonstrates a method to systematically reduce finite size effects in exact diagonalization studies of Hubbard models by integrating over boundary conditions, significantly improving accuracy of ground-state and thermodynamic property calculations.

Contribution

The authors introduce a grand-canonical boundary condition integration technique that effectively minimizes finite size corrections in Hubbard model simulations.

Findings

Finite size corrections are reduced by an order of magnitude.

The method improves ground-state property estimates.

Specific heat calculations are more accurate with the new approach.

Abstract

We study the possibility of controlling the finite size corrections in exact diagonalization studies quantitatively. We consider the one- and two dimensional Hubbard model. We show that the finite-size corrections can be be reduced systematically by a grand-canonical integration over boundary conditions. We find, in general, an improvement of one order of magnitude with respect to studies with periodic boundary conditions only. We present results for ground-state properties of the 2D Hubbard model and an evaluation of the specific heat for the 1D and 2D Hubbard model.