Slave bosons in radial gauge: a bridge between path integral and hamiltonian language

TL;DR

This paper bridges path integral and Hamiltonian approaches for strongly correlated electrons using slave boson representation in the radial gauge, providing exact analytical results for a two-site impurity model.

Contribution

It establishes a novel correspondence between world line resummation and Hamiltonian diagonalization in the slave boson framework, including spinful and spinless cases.

Findings

Green's functions of physical electrons and pseudofermions coincide in the spinless case

Exact analytical results for a two-site Anderson impurity model

Radial slave boson expectation value is finite and not related to Bose condensation

Abstract

We establish a correspondence between the resummation of world lines and the diagonalization of the Hamiltonian for a strongly correlated electronic system. For this purpose, we analyze the functional integrals for the partition function and the correlation functions invoking a slave boson representation in the radial gauge. We show in the spinless case that the Green's function of the physical electron and the projected Green's function of the pseudofermion coincide. Correlation and Green's functions in the spinful case involve a complex entanglement of the world lines which, however, can be obtained through a strikingly simple extension of the spinless scheme. As a toy model we investigate the two-site cluster of the single impurity Anderson model which yields analytical results. All expectation values and dynamical correlation functions are obtained from the exact calculation of the relevant functional integrals. The hole density, the hole auto-correlation function and the Green's function are computed, and a comparison between spinless and spin 1/2 systems provides insight into the role of the radial slave boson field. In particular, the exact expectation value of the radial slave boson field is finite in both cases, and it is not related to a Bose condensate.