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Computational and Theoretical Chemistry

Lowest energy states of Hubbard ladder model with infinite electron repulsion

Vladyslav O. Cheranovskii, E. V. Ezerskaya, Douglas J. Klein, V. V. Tokarev

Published Mar 23, 2017• 0 citations
Publisher
DOI
10.1016/j.comptc.2017.03.026

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We apply perturbation theory and cyclic spin permutation formalism to study the lowest energy states of the infinite-repulsion Hubbard model on n-leg ladders with alternating values of one-site energies αi for neighboring rungs.We establish the "ferromagnetic" character of ladder ground-state at electron densities in the interval 1 -(2n) -1 ≤ ρ ≤ 1 and sufficiently large alternation of one-site energies of neighbor rungs of the ladder.We also show the stability of this state against the small deviations of the values of αi in contrast to the case of two-leg ladder formed by weakly interacting neighbor rungs with equal one-site energies.
Low-energy states of the Hubbard model with infinite electron repulsion on an anisotropic triangular strip-type lattice formed by weakly interacting linear segments are studied. The estimates of the stability region boundaries for the ferromagnetic ground state of the lattice are obtained in first order perturbation theory in the interaction between the segments. It is shown that a magnetic transition accompanied by a jumpwise variation of the total spin of the ground state from the minimum to the maximum value is possible for lattices with cyclic boundary conditions and the number of electrons greater than the number of segments by unity.
For the Hubbard model with infinite-range hopping, a sensible competition between hopping and Hubbard repulsion can only be found when U/t scales with the volume of the system. Only two electrons carry all the kinetic energy and so the variations in Hubbard repulsion are bounded by only 2U for an eigenstate. To be comparable with the kinetic energy this must be extensive. For this case the author derives some exact eigenstates for the model. The lowest energy solution is paramagnetic although the spin degeneracy energy scale is very small. The behaviour of this system appears to be very different to that for the shorter-range hopping systems and so little can be deduced about more physical models.