Finite-temperature generalization of the ‘‘line and pole’’ decomposition for self-energies: Application to one-dimensional quantum wires

We present a method for obtaining expressions for the analytic continuation of finite-temperature self-energies which are suitable for use in numerical computations. In the case of the GW approximation for the self-energy, this method gives the finite-temperature generalization of the zero-temperature ``line and pole'' decomposition. This formalism is used to calculate the finite-temperature self-energy and band-gap renormalization of electrons in the extreme quantum limit of a quantum wire.