Recent Advances in the Calculation of Dynamical Correlation Functions

摘要: We review various theoretical methods that have been used in recent years to calculate dynamical correlation functions of many-body systems. Time-dependent and their associated frequency spectral densities are the quantities interest, for they play a central role both experimental understanding dynamic properties. In particular, appear fluctuation-dissipation theorem, where response system an external perturbation is given terms relaxation function unperturbed system, provided disturbance small. The method recurrence relation has, at its foundation, solution Heisenberg equation motion operator interacting system. For instance, absence pure exponential behavior any Hamiltonian relations was quantum systems such as dense electron gas, transverse Ising model, XY model with Dzyaloshinskii-Moriya interactions, well classical harmonic oscillator chains. Effects disorder were considered some those cases analytical solutions not feasible, approximation schemes used, but highly model-dependent. Another important approach numericallly exact diagonalizaton method. It finite-sized systems, which sometimes provides very reliable information dynamics infinite-size limit. this work, we discuss most relevant applications numerical calculations based on diagonalizations. relies coefficients continued fraction Laplace transformed function. calculation becomes involved and, only few offer solution. shall concentrate our efforts extrapolation must be obtain long times (or low frequency) regimes. also cover work diagonalization finite sized thermodynamically results identifies difficulties intrinsic relations.