Universality in the Hubbard model

Tadahiro Miyao

Published 2017-12-15Version 1

A new viewpoint of universality is introduced in strongly correlated electron systems; Our description relies on the operator theoretic correlation inequalities. We explain the Marshall-Lieb-Mattis theorem and Lieb\rq{}s theorem from a viewpoint of universality; in addition, from the new perspective, we prove that Lieb\rq{}s theorem still holds true even if the electron-phonon and electron-photon interactions are taken into account. We also study Nagaoka-Thouless\rq{} theorem and its stabilities in terms of universality.