Ferrimagnetism in the Hubbard, dimmer-connector frustrated chain

Abstract

We study the AB 2 "dimmer-connector" chain within a generalized Hubbard model, which contains sitedependent parameters, and different chemical potentials for A and B sites. Considering one electron per atom, we carry out exact calculations for finite clusters, and derive some asymptotic results, valid for macroscopic chains. We take a non-vanishing intra-dimmer electron hopping, thus departing from the condition of a bipartite lattice. In spite of that, the system persists ferrimagnetic in some region of the parameter space, thus generalizing a theorem of Lieb for bipartite lattices. A somewhat surprising result is that the ferrimagnetic phase is possible, even for a very large chemical potential jump between A and B sites. In another respect, we show that a previously reported macroscopic (2 N ) degenerancy of the AB 2 Heisenberg chain ground state (GS) is fully removed on going to the (more fundamental) Hubbard model, yielding a non-magnetic GS.

Geometrical frustration of an extended Hubbard diamond chain in the quasiatomic limit

“…inside braces we mean the least integer of any real number. Thereafter, all elements of matrix (20) are well expressed just in terms of w 0,0 (x). The Boltzmann factors for the effective Hubbard model (18) with three and four-body terms are given by: w 0,0 = A, w 0,1 = Ar; r = e βμ/2 , w 0,2 = Ars; s = e −βŨ/2 , w 1,1 = Ar 2 t; t = e −βṼ , w 1,2 = Ar 3 st 2 u; u = e −βW3/2 , w 2,2 = Ar 4 s 2 t 4 u 4 v.…”

“…As the particles interact, it leads to the strong localization induced by the magnetic field for the particular value of a flux. Analogous model was also studied by Rossler and Mainemer 20 . The Hubbard model in other quasione-dimensional triangular structure also was studied by Wang 21 .…”