Study of linear response in Hubbard chains using Manybody Perturbation Theory
In this work the basic formalism of nonequilibrium Green’s functions is presented and then applied to study a Ward identity in linear response theory, namely the frequency sumrule. It can be proven that the frequency sumrule is satisfied when the quantities involved are calculated using perturbation theory within a conserving approximation for the selfenergy. To illustrate this equality
along with other properties of the response function, a numerical application that solves the KadanoffBaym equations for systems of Hubbard chains was used. The results showed that the frequency sumrule was satisfied to the same extent by all the conserving approximations used as by the exact diagonalization numerical results. The density response function was analyzed diagrammatically
for a series of conserving approximations for the selfenergy and this demonstrated that even for a first order in perturbation theory approximation for the selfenergy, the response function has a corresponding complex, third order in the perturbation diagrammatic structure.
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