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A formally exact one-frequency-only Bethe-Salpeter-like equation. Similarities and differences between GW+BSE and
Valerio Olevano1, Julien Toulouse2, Peter Schuck1
1Université Grenoble Alpes, 38000 Grenoble, France.
Abstract:
A formally exact Bethe-Salpeter-like equation for the linear-response function is introduced with a kernel which depends only on the one frequency of the applied field. This is in contrast with the standard Bethe-Salpeter equation (BSE) which involves multiple-frequency integrals over the kernel and response functions. From the one-frequency kernel, known approximations are straightforwardly recovered. However, the present formalism lends itself to more powerful approximations. This is demonstrated with the exact analytical solution of the Hubbard molecule. Similarities and differences of the GW + BSE approach with the self-consistent random-phase approximation are also discussed.
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