A coefficient average approximation towards Gutzwiller wavefunction formalism

TL;DR

This paper introduces a new coefficient average approximation for evaluating expectation values in Gutzwiller wavefunctions, showing improved accuracy on finite systems and asymptotic equivalence to the standard Gutzwiller approximation on infinite systems.

Contribution

A novel approximation method for Gutzwiller wavefunctions that enhances evaluation accuracy for finite systems and aligns with existing methods asymptotically for infinite systems.

Findings

Outperforms standard Gutzwiller approximation on finite systems

Approaches Gutzwiller approximation asymptotically for infinite systems

Supports potential extensions to multiband systems

Abstract

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.