INTERMEDIATE-COUPLING THEORY OF THE SPIN POLARON IN THE T-J MODEL

The spin polaron in the t-J model, i.e., a hole dressed by a cloud of virtual magnons of the antiferromagnetic spin background, is treated w ithin the framework of intermediate-coupling theory. To this end the o riginal t-J model is first reformulated in terms bf spinless fermions and bosons by means of the generalized Dyson-Maleev representation (DM R). The latter may be regarded as the natural extension of the ordinar y DMR of pure (undoped) spin systems to the case where holes are prese nt, and is similar to the one originally proposed by Schmitt-Rink, Var ma, and Ruckenstein. The reformulated t-J model, which is reminiscent of the Frohlich Hamiltonian, is then subjected to a series of unitary transformations, analogous to those employed by Lee, Low, and Pines in their treatment of the Frohlich polaron. Our approach yields an appro ximate quasiparticle energy E(k) as well as the corresponding eigenvec tor. To explore the range of validity of the theory presented here, th e analytic expressions are then further analyzed for intermediate (J/t =0.4) and strong (J/t=0.08) coupling, where special attention is paid to the quasiparticle bandwidth W. The intermediate-coupling result for E(k) is in excellent agreement with the dispersion curve recently obt ained by Dagotto and co-workers by means of a Green function Monte Car lo method. Surprisingly, even in the strong-coupling range the bandsha pe remains qualitatively correct. The bandwidth W is rather accurate f or weak coupling (J/t>3), as expected, and still reasonable in the int ermediate range 0.4 less than or similar to J/t less than or equal to 3, where it deviates from the correct values by some 10-20%. Our theor y fails, however, to describe the proper behavior of W in the strong-c oupling regime. This shows that the limitations of our approach manife st themselves in the bandwidths rather than in the shapes of the dispe rsion curves. Our conclusion is that intermediate-coupling theory is a ppropriate for J/t greater than or similar to 0.4, whereas a genuine s trong-coupling theory is required for all other cases.