A Variational Moments Approach to the One Dimensional Hubbard Model

In this work we shall study the one dimensional Hubbard model% \[ H=t\sum_{,\sigma}\left( c_{i\sigma}^{\dag}c_{j\sigma}+c_{j\sigma}^{\dag }c_{i\sigma}\right) +U\sum_{i}n_{i\uparrow}n_{i\downarrow}% \] using both a connected moments approach as well as a Lanczos tridiagonal scheme. Following the work of Eichenberger and Baeriswyl (PRB 76, 180504(R), 2007) we use a modified variational wavefunction which includes the hopping term of the Hamiltonian. Our results show a marked improvement in our estimation of the ground-state energy in the region of intermediate coupling $t/U\approx0.1$.