Solutions to the multiple-component 1/rHubbard model

Strong excitons in novel two-dimensional crystals: Silicane and germanane

“…Results. -The ground-state geometries (see footnote 1 ) of graphane, silicane and germanane, reported in table 1, are in agreement with other DFT calculations [4,7,22,23,[32][33][34], and with the available experimental data [6,[18][19][20]35,36].…”

“…Interestingly, such H-saturated Si and Ge sheets have been synthesized a long time ago in the form of layered polysilane [18,19] or layered polygermyne [20] and have also been investigated [21]. The properties of the individual sheets are however little known.…”

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].…”

Invariants of the 1/r 2 Supersymmetric t-J Models

“…Since the independent works by Haldane and Shastry, there have been renewed interests in exactly solvable models of long range interaction [1][2][3][4][5][6][7][8][9][10][11][12][14][15][16][17]. Of these systems, the 1D supersymmetric t-J model of 1/r 2 exchange and hopping has been studied intensively [6][7][8]15].…”