Density matrix renormalization group analysis of the Nagaoka polaron in the two-dimensional t-J model -: art. no. 024411

It is widely believed that a single hole in the two- (or three-)dimensional t-J model, for sufficiently small exchange coupling J, creates a ferromagnetic bubble around itself, a finite J remnant of the ferromagnetic ground state at J=0 (the infinite U Hubbard model), first established by Nagaoka [Phys. Rev. 147, 392 (1966)]. We investigate this phenomenon in two dimensions using the density matrix renormalization group, for system sizes up to 9 x 9. We find that the polaron forms for J/t < 0.02-0.03. Although finite-size effects appear large, our data seems consistent with the expected 1.1(J/t)(-1/4) variation of polarion radius. We also test the Brinkman-Rice model of nonretracing paths in a Neel background, showing that it is quite accurate, at larger J. Results are also presented in the case where the Heisenberg interaction is dropped (the t-J(z) model). Finally we discuss a "dressed polaron" picture in which the hole propagates freely inside a finite region but makes only self-retracing excursions outside this region.