Derivation of thet−Jmodel for finite doping

Abstract

Mapping complex problems to simpler effective models is a key tool in theoretical physics. One important example in the realm of strongly correlated fermionic systems is the mapping of the Hubbard model to a t-J model which is appropriate for the treatment of doped Mott insulators. Charge fluctuations across the charge gap are eliminated. So far the derivation of the t-J model is only known at half-filling or in its immediate vicinity. Here we present the necessary conceptual advancement to treat finite doping. The results for the ensuing coupling constants are presented. Technically, the extended derivation relies on self-similar continuous unitary transformations (sCUT) and normal-ordering relative to a doped reference ensemble. The range of applicability of the derivation of t-J model is determined as function of the doping δ and the ratio bandwidth W over interaction U .

Effective models for Anderson impurity and Kondo problems from continuous unitary transformations

“…To this end, we introduce an operator basis whose terms imply a unambiguous change of local energy on the impurity. The chosen operator basis has already been used successfully before in the derivation of generalized t-J models from Hubbard models 40 . Its terms are shown in Tab.…”

“…This amounts up to the Schrieffer-Wolff transformation realized by CUTs 30 or the systematic derivation of t-J models from Hubbard models by CUTs 40 . We choose the generator…”

“…The flow equation (2) is the heart of the CUT approach. There are numerous ways to choose the generator 33,38,40,42,45,46 . We will discuss later which kind of generator is employed in the present work.…”

Orientational bond and Néel order in the two-dimensional ionic Hubbard model

“…Such terms, occurring already in the second order in t with positive sign, have a singlet on a bond inx-direction hop to a bond inŷ-direction 24 . This correlated hopping corresponds to the well-known threesite terms in the t-J model [14][15][16][17] . If the wave function has the opposite sign onŷ-bonds of those onx-bonds this correlated hopping leads to attraction and eventually to a bound state with d-wave symmetry.…”

“…In this way, an effective model is derived in terms of the elementary fermionic QPs. The virtual processes are eliminated as in the derivation of a t-J model from a Hubbard model [14][15][16][17] . The effective model allows us to address the interaction of two of these QPs.…”