On the evaluation of matrix elements in partially projected wave functions

TL;DR

This paper extends the Gutzwiller approximation to evaluate matrix elements between ground and excited states, using normalization techniques and Monte Carlo methods, revealing novel local density oscillations.

Contribution

It introduces a generalized scheme for calculating matrix elements in partially projected wave functions, combining analytical and Monte Carlo approaches.

Findings

Analytical and VMC evaluation of normalization for projected Fermi sea

Observation of oscillations in hole density near the reservoir site

Extension of Gutzwiller approximation to excited states

Abstract

We generalize the Gutzwiller approximation scheme to the calculation of nontrivial matrix elements between the ground state and excited states. In our scheme, the normalization of the Gutzwiller wave function relative to a partially projected wave function with a single non projected site (the reservoir site) plays a key role. For the Gutzwiller projected Fermi sea, we evaluate the relative normalization both analytically and by variational Monte-Carlo (VMC). We also report VMC results for projected superconducting states that show novel oscillations in the hole density near the reservoir site.