A coefficient average approximation towards Gutzwiller wavefunction formalism

Gutzwiller wavefunction is a physically well motivated trial wavefunction for describing correlated electron systems. In this work, a new approximation is introduced to facilitate evaluation of the expectation value of any operator within the Gutzwiller wavefunction formalism. The basic idea is to make use of a specially designed average over Gutzwiller wavefunction coefficients expanded in the many-body Fock space to approximate the ratio of expectation values between a Gutzwiller wavefunction and its underlying noninteracting wavefunction. To check with the standard Gutzwiller approximation (GA), we test its performance on single band systems and find quite interesting properties. On finite systems, we noticed that it gives superior performance than GA, while on infinite systems it asymptotically approaches GA. Analytic analysis together with numerical tests are provided to support this claimed asymptotic behavior. At the end, possible improvements on the approximation and its generalization towards multiband systems are illustrated and discussed.