Study of linear response in Hubbard chains using Many-body Perturbation Theory

2010

In this work the basic formalism of non-equilibrium Green’s functions is presented and then applied to study a Ward identity in linear response theory, namely the frequency sum-rule. It can be proven that the frequency sum-rule is satisfied when the quantities involved are calculated using perturbation theory within a conserving approximation for the self-energy. To illustrate this equality along with other properties of the response function, a numerical application that solves the Kadanoff-Baym equations for systems of Hubbard chains was used. The results showed that the frequency sum-rule was satisfied to the same extent by all the conserving approximations used as by the exact diagonali…