Analytical approach to the t—t′—J model: Quasi-particle dispersion, Fermi surface and optical conductivity

An approximate, analytically solvable ansatz for the self-energy of a single hole in the 2-dimensional t—t′—J model, at t J, t′, is proposed: M2q,Q Q(f(ω)+iΓ(ω)). It features consistently: 1) the incoherence of a substantial part of the hole spectral weight, asymmetrically stretched over an energy interval of width t; 2) the collective nature of the quasi-particle dispersion, (q), with q-dependence generated by the spin-hole scattering matrix element, and 3) the enhancement of the quasi-particle mass, m* (Jln(t/J))−1, i.e. a renormalization of the quasi-particle bandwidth: Jln(t/J). Our analytical result for (q) is in good accord with existing numerical data for the t-J model. Calculated optical conductivity exhibits single-hole/multimagnon resonances superimposed on a 1/ω tail of width t. A change of the curvature of the Fermi surface from hole-like to electron-like with doping is also found.