The extended mean-field approximation

Ning-Hua Tong

The variational cluster approximation (VCA) proposed by M. Potthoff et al. [Phys. Rev. Lett. 91, 206402 (2003)] is extended to electron or spin systems with nonlocal interactions. By introducing more than one source field in the action and employing the Legendre transformation, we derive a generalized self-energy functional with stationary properties. Applying this functional to a proper reference system, we construct the extended VCA (EVCA). In the limit of continuous degrees of freedom for the reference system, EVCA can recover the cluster extension of the extended dynamical mean-field theory (EDMFT). For a system with correlated hopping, the EVCA recovers the cluster extension of the dynamical mean-field theory for correlated hopping. Using a discrete reference system composed of decoupled three-site single impurities, we test the theory for the extended Hubbard model. Quantitatively good results as compared with EDMFT are obtained. We also propose VCA (EVCA) based on clusters with periodic boundary conditions. It has the (extended) dynamical cluster approximation as the continuous limit. A number of related issues are discussed.

Diego Luis González, Alberto Pimpinelli, T. L. Einstein

We propose a mean-field method to calculate approximately the spacing distribution functions p((n))(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p((n))(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.

S. N. Coppersmith, P. B. Littlewood

Models of strongly interacting Fermi systems are sufficiently intractable that simple mean-field approximations (typically Hartree-Fock) are often employed to obtain qualitative insight into their properties, and also to set parameter values by comparing with band-structure calculations. However, if the correlations are accounted for with use of more sophisticated (but still mean-field-like) methods, qualitative changes in charge densities and magnetic properties can result. We compare four ``mean-field'' approximations for an extended Hubbard model and show that they yield quite different results. Implications for the choice of model for high-temperature superconductors are discussed.

Andreas Wipf