Intermediate-coupling theory of the spin polaron in the t-J model.

Abstract

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 within the framework of intermediate-coupling theory. To this end the original t-J model is first reformulated in terms of spinless fermions and bosons by means of the generalized Dyson-Maleev representation (DMR). The latter may be regarded as the natural extension of the ordinary DMR of pure (undoped) spin systems to the case where holes are present, and is similar to the one originally proposed by Schmitt-Rink, Varma, and Ruckenstein. The reformulated t-J model, which is reminiscent of the Fr\"ohlich Hamiltonian, is then subjected to a series of unitary transformations, analogous to those employed by Lee, Low, and Pines in their treatment of the Fr\"ohlich polaron. Our approach yields an approximate quasiparticle energy E(k) as well as the corresponding eigenvector. To explore the range of validity of the theory presented here, the 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 obtained by Dagotto and co-workers by means of a Green function Monte Carlo method. Surprisingly, even in the strong-coupling range the bandshape remains qualitatively correct.The bandwidth W is rather accurate for weak coupling (J/t\ensuremath{\gtrsim}3), as expected, and still reasonable in the intermediate range 0.4\ensuremath{\lesssim}J/t\ensuremath{\le}3, where it deviates from the correct values by some 10--20 %. Our theory fails, however, to describe the proper behavior of W in the strong-coupling regime. This shows that the limitations of our approach manifest themselves in the bandwidths rather than in the shapes of the dispersion curves. Our conclusion is that intermediate-coupling theory is appropriate for J/t\ensuremath{\gtrsim}0.4, whereas a genuine strong-coupling theory is required for all other cases. \textcopyright{} 1996 The American Physical Society.