Coherent motion of a hole in a two-dimensional quantum antiferromagnet

Abstract

The dispersion relation for the coherent propagation of a hole moving in a two-dimensional quantum antiferromagnet is discussed. The system is described by two model Hamiltonians, thet-J model and thet-t′-J model, which have been used frequently to discuss strong electron-correlation effects present in high-T c superconductors. The calculations are based on the introduction of a new wave function which is constructed by use of equations derived by Shraiman and Siggia. The different mechanisms for the coherent propagation, which are due to the spin fluctuation and the hopping terms of the Hamiltonian, are treated on the same footing. As a result of the inclusion of an effective hopping mechanism along spiral paths-first discussed by Trugman-the minimum of the band is somewhat changed compared to results recently obtained in the literature. For large values of the ratiot/J an inversion of the whole dispersion relation occurs. The overall shapes of the dispersion within both models are found to agree quite well, though for small values oft/J the bandwidth within thet-J model becomes significantly smaller than that of thet-t′-J model.