Renormalization of transition matrix elements of particle number operators due to strong electron correlation

TL;DR

This paper analytically derives how electron correlation renormalizes impurity effects and transition matrix elements in strongly correlated systems, revealing different behaviors for magnetic and non-magnetic impurities and correcting previous treatment errors.

Contribution

It provides an improved Gutzwiller approximation-based analysis of impurity renormalization, highlighting different effects on transition matrix elements and correcting prior errors in charge interaction treatment.

Findings

Non-magnetic impurities are weakened by the same factor as hopping.

Magnetic impurities are strengthened by the square root of the spin-exchange factor.

Second order transition matrix elements are strongly suppressed.

Abstract

Renormalization of non-magnetic and magnetic impurities due to electron double occupancy prohibition is derived analytically by an improved Gutzwiller approximation. Non-magnetic impurities are effectively weakened by the same renormalization factor as that for the hopping amplitude, whereas magnetic impurities are strengthened by the square root of the spin-exchange renormalization factor, in contrast to results by the conventional Gutzwiller approximation. We demonstrate it by showing that transition matrix elements of number operators between assumed excited states and between an assumed ground state and excited states are renormalized differently than diagonal matrix elements. Deviation from such simple renormalization with a factor is also discussed. In addition, as related calculation, we correct an error in treatment of renormalization of charge interaction in the literature. Namely, terms from the second order of the transition matrix elements are strongly suppressed. Since all these results do not depend on the signs of impurity potential or charge interaction parameter, they are valid both in attractive and repulsive cases.