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International Journal of Quantum Chemistry

Excitation spectrum of Hubbard model with infinite electron repulsion on strip-type triangular lattices

Vladyslav O. Cheranovskii, E. V. Ezerskaya, M. V. Krikunov

Published Jan 1, 2001• 3 citations
Publisher

Abstract

The estimations of the stability region of the lattice ferromagnetic ground state in the space of model parameters are found. For the triangular lattice strip formed by L segments with the total number of electrons N=L+1 we derived the effective Hamiltonians describing the low-energy states of the strips and obtained the analytical estimations for above stability region. The possibility of the magnetic transition with the jump of the ground-state spin between minimal and maximal values has also been shown. For the strip with N=L and an alternating value of the one-site potential energy, we have obtained the exact relation between electron parameters, which provides the ferromagnetic character of the lattice ground state. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 253–259, 2001

DOI
10.1002/1097-461x(2001)81:4<253::aid-qua2>3.0.co;2-h

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The estimations of the stability region of the lattice ferromagnetic ground state in the space of model parameters are found. For the triangular lattice strip formed by L segments with the total number of electrons N=L+1 we derived the effective Hamiltonians describing the low-energy states of the strips and obtained the analytical estimations for above stability region. The possibility of the magnetic transition with the jump of the ground-state spin between minimal and maximal values has also been shown. For the strip with N=L and an alternating value of the one-site potential energy, we have obtained the exact relation between electron parameters, which provides the ferromagnetic character of the lattice ground state. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 253–259, 2001
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.
We study the dependence of the ground state spin of a multiband Hubbard model with infinite electron repulsion on anisotropic triangular and rectangular lattice strips on the model parameters. Considering the results of numerical calculations for the exact spectra of finite triangular lattice strips at different values of hopping integrals, we show the existence of a type of magnetic transitions with the jump of the ground state spin between minimal and maximal values. This transition is found only for special filling factors and when the lattice anisotropy parameter takes some critical value, which depends on the size of the lattice strip. Near this critical point two states with marginal values of the total spin, both of which can be a ground state before or after the transition, are locally stable against a few flips of spins.
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.
The Hubbard Hamiltonian with infinite on-site repulsion and negative transfer is diagonalized numerically on 3×3 frustrated lattices, such as the square lattice with next-nearest-neighbor transfer and the triangular lattice. The number of electrons is chosen to be less by just one electron than that in the exactly half-filled band. When the strength of the frustration is sufficiently large, a singlet state appears as the ground state. Then, the total spin of the lowest excited state is unity. There is an excitation gap for the square lattice but not for the triangular lattice.
All the energy eigenvalues of the Hubbard model with infinite repulsion on 2×2×2 cubic lattice for different electron numbers N e are calculated numerically. For N e =4, 7 the ground state is completely ferromagnetic; namely, total spin S is N e /2. For N e =5, the total spin of the ground state is 3/2. For N e =2, 6, it is zero. For N e =1, 3, it is 1/2. Thermodynamic quantities such as entropy, susceptibility and specific heat are calculated with the method of canonical ensemble. There are two peaks in the specific heat curve for N e =4, 5, 6, 7, but only one peak for N e =1, 2, 3.