Date of Original Version
We use the recursion method to study the spectral and dynamical properties of the one-dimensional (1D) s=1/2 XXZ method with planar anisotropy at T=0. Distinct methods of continued-fraction analysis have been developed for the weak-coupling and strong-coupling regimes of the corresponding lattice fermion system. The weak-coupling analysis presented here yields detailed information on the spectral-weight distribution in dynamic structure factors and spin autocorrelation functions, notably on the infrared singularities produced by critical fluctuations, and on the bound states for the case of attractive fermion interaction. The same method is then applied to the charge dynamics of the 1D t-J model for strongly correlated electrons. There it yields similar yet distinct results in the regime of weak exchange coupling. The results for renormalized bandwidths of particle-hole excitations are consistent with available results for charge velocities, and the results for the infrared exponent in the charge dynamic structure factor agree with existing results for the exponent of the equal-time charge correlation function.
V.S. Viswanath, Shu Zhang, Gerhard Müller and Joachim Stolze Zero-temperature dynamics of the one-dimensional XXZ and t-J models: a weak-coupling continued-fraction analysis. Phys. Rev. B 51 (1995), 368-380. Available at: http://dx.doi.org/10.1103/PhysRevB.51.368