Variational investigation of low dimensional correlated electron systems via the limit of high dimensions

Abstract

We show that the limit of large dimensions (d=∞) can be used to obtain accurate variational results even for low dimensional (d=1, 2) fermionic systems, such as the Hubbard model or the periodic Anderson model. Using explicit correlated variational wave functions this is achieved by evaluating the expectation values for d=∞ with the correct d-dimensional density of states and including 1/d-corrections. For example, an application of this approach to the periodic Anderson model in d=1 shows that the result for the ground state energy, the momentum distributions of c- and f-electrons, and the spin-spin and density-density correlations functions for the f-electrons are in excellent agreement with the variational Monte Carlo data of Shiba.