Gutzwiller-Jastrow wave functions for the 1/rHubbard model

Exact ground state correlations in the supersymmetric exchange t-J model

“…However, the forms of the integrands do not allow any immediate interpretation in terms of the form factors for the elementary excitations. This is also true of the expressions obtained from random matrix theory for the static two-body correlation of the Calogero-Sutherland model at λ = 2 [15], which is the limiting case of (6b) when ρ ↓ = 0. It wasn't until the discovery of a new integral representation [3] that an interpretation in terms of the form factors for the elementary excitations became possible [1].…”

The Yangian symmetry of the Hubbard models with variable range hopping

“…After a canonical transformation c jσ → i j c jσ we recover the Yangian generator of Uglov and Korepin [3]. In the limit U → ∞ at less than half filling the model reduces to the "t-0" chain [12] with all states with double occupancies projected out from the Hilbert space. Because at half filling hopping is not allowed anymore in this limit, one can set S 0 j = 1, and recover the Yangian generator of the Haldane-Shastry chain [7] or its hyperbolic counterpart to leading order in (t/U) 2 .…”

“…A first application of our new Y(sl 2 ) Yangian will be the classification of the Jastrowlike eigenfunctions of the "t-0" model [12]. For the system at finite on-site energy the situation is more complicated.…”

Exact results of the one-dimensional 1/r2supersymmetrict-Jmodel without translational invariance

“…In one dimension, however, the Bethe-ansatz technique may allow us to exactly solve Hamiltonians in some special cases, such as the Lieb-Wu solution [2] and the ordinary t-J model at its supersymmetric point [3]. In particular, the 1D long range exactly solvable electronic models have attracted a lot of attention, since they display interesting physics with solutions of simple mathematical structure [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]. Recently, we have been able to explicitly construct all the constants of motion for the translational invariant long range supersymmetric t-J model, by mapping the system to a mixture of fermions and bosons, with the super-algebra representation for the electron fields [12].…”