Extended Gutzwiller Approximation for Inhomogeneous System

TL;DR

This paper extends the Gutzwiller approximation to inhomogeneous systems by including spin-and-site-dependent fugacity factors, clarifying previous inconsistencies and analyzing symmetry breaking effects with comparisons to Monte-Carlo results.

Contribution

It introduces a generalized Gutzwiller approximation with fugacity factors for inhomogeneous systems and discusses symmetry restoration schemes validated against Monte-Carlo data.

Findings

Fugacity factors reconcile different Gutzwiller factor choices.

Gutzwiller approximation breaks rotational symmetry.

Different spin components require separate renormalization.

Abstract

The generalization of the Gutzwiller approximation to inhomogeneous systems is considered, with extra spin-and-site-dependent fugacity factors included. It is found that the inclusion of fugacity factors reconciles the seemingly contradictory choices of Gutzwiller factors used in the literature. Moreover, from the derivation of the Gutzwiller factors, it is shown that the Gutzwiller approximation breaks the rotational symmetry of the trial wavefunctions, and that different components of the spin-spin interaction need to be renormalized differently under the approximation. Various schemes to restore the rotational symmetry are discussed and are compared with results from variational Monte-Carlo calculations for the two-dimensional square-lattice antiferromagnet. Results along different paths within the full parameter space, which corresponds to different choices of fugacity factors in the literature, are also compared.