Optical absorption and single-particle excitations in the two-dimensional Holstein $t-J$ model

To discuss the interplay of electronic and lattice degrees of freedom in systems with strong Coulomb correlations we have performed an extensive numerical study of the two-dimensional Holstein $t-J$ model. The model describes the interaction of holes, doped in a quantum antiferromagnet, with a dispersionsless optical phonon mode. We apply finite-lattice Lanczos diagonalization, combined with a well-controlled phonon Hilbert space truncation, to the Hamiltonian. The focus is on the dynamical properties. In particular we have evaluated the single-particle spectral function and the optical conductivity for characteristic hole-phonon couplings, spin exchange interactions, and phonon frequencies. The results are used to analyze the formation of lattice hole polarons in great detail. Links with experiments on layered perovskites are made. In addition, we compare the Chebyshev recursion and maximum entropy algorithms, used for calculating spectral functions, with standard Lanczos methods.