Path-integral approach to the Hubbard model

Abstract

A path-integral approach to the Hubbard model is developed for the whole range of the coupling strength U. At half filling, the strong-coupling results are readily reproduced within the simple Gaussian fluctuations.The low-lying spin wave is shown to be described by the nonlinear a (2) it also agrees with the t-J-model result. The present method provides a starting point to approach the finitedoping problem.

One-dimensional large-UHubbard model: An analytical approach

“…The equivalence between the present formalism and the t-J model will be discussed elsewhere [7,9]. Now there is only one auxiliary n; field left in Lagrangian (2) [7]. In the case of U»t, the localized picture will be more convenient for our discussion and we could write down this transformation in the lattice representation as Ho= -Jg (a; a; -P;P;)+UgP; P; -2 Jg (a; a;+2 -P; P;+2+H c.), (6) where J= 2t /-U.…”

“…In this case, to the order of t/U, the charge and amplitude fluctuations at the occupied sites in which the spinor a; is related to the electron operator c;=(c;t,c;l) through are negligible [7,9], and p; and A; could be safely replaced by their mean-field values p; =&= -iU/2 and A; =( -1)'A=( -1)'U/2, with a full local (staggered) moment m; =2k;/U=( -1)'. The equivalence between the present formalism and the t-J model will be discussed elsewhere [7,9]. Now there is only one auxiliary n; field left in Lagrangian (2) [7].…”

“…The elementary excitations of charge and spin together with all the important correlation functions will be analytically derived. The path-integral formalism used here has been developed previously to study the two-dimensional Hubbard model [7,8].…”

“…In the strong-coupling regime, as the result of the suppression of the double occupancy, the spin at the occupied site becomes fully polarized and is determined by the direction n;. In this case, to the order of t/U, the charge and amplitude fluctuations at the occupied sites in which the spinor a; is related to the electron operator c;=(c;t,c;l) through are negligible [7,9], and p; and A; could be safely replaced by their mean-field values p; =&= -iU/2 and A; =( -1)'A=( -1)'U/2, with a full local (staggered) moment m; =2k;/U=( -1)'. The equivalence between the present formalism and the t-J model will be discussed elsewhere [7,9].…”

“…The Lagrangian (7) shows that the hole could get the largest hopping matrix ( = t ) when ( it from the operator formalism).…”