Properties of the Gutzwiller Wavefunction

B. Sriram Shastry, T. V. Ramakrishnan

Jun Liu, Yongxin Yao, Cai‐Zhuang Wang +1 more

Gutzwiller wavefunction is a physically well-motivated trial wavefunction for describing correlated electron systems. In this work, a new approximation is introduced to facilitate the 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 over GA, while on infinite systems it asymptotically approaches GA. Analytic analysis together with numerical tests are provided to support this claimed asymptotical behavior. Finally, possible improvements on the approximation and its generalization towards multiband systems are illustrated and discussed.

Balázs Hetényi, Hans Gerd Evertz, Wolfgang von der Linden

The Gutzwiller approximate solution to the Gutzwiller wavefunction yields exact results for the Gutzwiller wavefunction in the infinite-dimensional limit. Implicit in the Gutzwiller approximation is an approximate local form of the fermion exchange hole. This approximate form is the same for all dimensions but is incorrect except in infinite dimensions. We implement the correct form for the exchange hole into the Gutzwiller approximation. We perform calculations on the one-dimensional Hubbard model at half-filling. They indicate that the implementation of the exchange hole already brings the Gutzwiller approximation into very close quantitative agreement with the results of the full Gutzwiller wavefunction. Metallicity as well as antiferromagnetism are recovered.

Florian Gebhard, Martin C. Gutzwiller

D. K. Sunko

Balázs Hetényi

The Drude and superfluid weights are investigated in the context of variational theory. It is shown that a commonly applied procedure to obtain the Drude weight actually corresponds to the superfluid weight. This realization changes previous interpretations of conductivity for variational wavefunctions, one result being that the Gutzwiller wavefunction displays a finite superfluid weight at finite interaction. To gain insight into DC conductivity an expression for the current response in terms of a geometric phase is derived. Applying to the Gutzwiller wavefunction it is shown that for any value of the interaction the Gutzwiller wavefunction is a perfect conductor.