Hole motion in quantum antiferromagnets: String and hopping results.

Abstract

We have investigated the {ital t}-{ital J} model and its variants using the string basis (of Shraiman, Siggia, Emery, and Lin) and the hopping basis (of Trugman); both bases are generated by the hopping term in the Hamiltonian applied repeatedly to the Neel state with a single hole. For the string basis, states to order {ital t}{sup 10} are treated exactly, so that the Green function is obtained to order {ital t}{sup 20}; the tree approximation (of Brinkman and Rice) is used for the remainder. The hopping basis, which relaxes constraints imposed in the string basis, contains all states generated by up to eight hops. Properties studied include the wave function, the ground-state energy, the effective mass, the bandwidth, the spectral function, the self-energy, and the density of states. For the {ital U}={infinity} model, there are no quasiparticles; the ferromagnetic polaron is missed. For the {ital t}-{ital J}{sub {ital z}} model, both the string and hopping bases provide excellent results for {ital J}{sub {ital z}}{gt}0.1{ital t}. The Ising limit of the {ital t}-{ital J} model is treated well by the string basis, but the Heisenberg limit {ital J}{sub {perpendicular}}={ital J}{sub {ital z}} requires the hopping basis, which gives apparently goodmore » results for all {ital J}{gt}0.1{ital t}. The mass is highly anisotropic; for example, at {ital J}=0.4{ital t} the masses parallel and perpendicular to the magnetic zone face are {ital m}{sub N}=20.4{ital m} and {ital m}{sub {perpendicular}}=2.1{ital m}.« less