Univ. Caen
A correspondence between the resummation of world lines and the diagonalization of the Hamiltonian for a strongly correlated electronic system is established[1]. 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. In addition, the exact expectation value of the radial slave boson field is finite in both cases, and it is not related to a Bose condensate. These considerations are then extended to the Kotliar-Ruckenstein representation, and further extended to systems involving non-local interaction terms[3,4]. We show that, within saddlepoint evaluation,ground state and all excitation levels agree with the exact diagonalization results. Thermodynamics and correlation functions maybe recoveredi in a suitably renormalized saddlepoint evaluation[3].
[1]R. Frésard, H. Ouerdane, and T. Kopp, Nucl. Phys. B 785, 286(2007).
[2]R. Frésard and T. Kopp, Nucl. Phys. B 594, 769(2001).
[3]R. Frésard and T. Kopp, Phys. Rev. B. 78, 073108(2008).
[4]R. Frésard, H. Ouerdane, and T. Kopp, Europhys. Lett. 82, 31001(2008).