Exact Results in Quantum Theory

In the first part of the talk I will discuss how the basic and best known models of the correlated electron systems are related to each other: Hubbard, t-J [1], Heisenberg, and Kugel-Khomskii spin-orbital models. Next, I will show the 1:1 correspondence between the spectral function of the t-J model and a particular Kugel-Khomskii spin-orbital model [2]. This latter feature has important consequences for the understanding of the recent spectroscopic experiments performed on transition metal oxides.[1] J. Spalek was recently awarded the FNP prize for the "distinguished contribution to the world of physics in 1977 when he derived for the first time the so-called t-J model" [K. A. Chao, J. Spalek, A. M. Oles, J. Phys. C 10, L271 (1977)].[2] Phys. Rev. Lett. 107, 147201 (2011); Phys. Rev. B 91, 165102 (2015).