Open Physics

Ferromagnetism in the two-dimensional Hubbard model with long-range hopping

Pavol Farkašovský, Hana Čenčariková

Published Oct 17, 2012• 4 citations

Abstract

Abstract The combination of small-cluster exact-diagonalization calculations and the quantum Monte Carlo method is used to examine ferromagnetism in the two-dimensional Hubbard model with a generalized type of hopping. It is found that the long-range hopping with exponentially decaying hopping amplitudes t ij ∼ − q Ri−Rj stabilizes the ferromagnetic state for a wide range of electron interactions U and electron concentrations n > 1. The critical value of the hopping parameter q c above which the ferromagnetic state becomes stable is calculated numerically and the ground-state phase diagram of the model is discussed for physically the most interesting cases.

DOI: 10.2478/s11534-012-0135-7

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Open Physics

Ferromagnetism in the two-dimensional Hubbard model with long-range hopping

Pavol Farkašovský, Hana Čenčariková

Published Oct 17, 2012• 4 citations

Publisher

Abstract

DOI: 10.2478/s11534-012-0135-7

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{U}_{c}(q)

above which the ferromagnetic state becomes stable is calculated numerically and the ground-state phase diagram of the model (in the $U\ensuremath{-}q$ plane) is presented for physically the most interesting cases.

U

and electron concentrations

n

. The critical value of magnetic field

h

below which the ferromagnetic state becomes unstable is calculated numerically. It is shown that below this critical value the ferromagnetic state breaks down into a metallic state for weak coupling and an insulating state for strong coupling. The phase diagram of the model in the $h\ensuremath{-}U$ plane is presented for physically the most interesting cases.

We study the magnetic properties of the two-dimensional Hubbard model with nearest-neighbor (t) and next-nearest-neighbor (

{t}_{2}

) hopping and on-site repulsion U. We first calculate the mean-field phase diagram as a function of band filling and U. Because of the Van Hove singularity in the density of states, we find a ferromagnetic phase extending to zero U for certain band filling. For the half-filled band case, antiferromagnetism sets in at a finite value of U if

{t}_{2}

\ensuremath{\ne}0. We study the behavior of spin-spin correlation functions for small lattices of up to N=64 atoms using Monte Carlo simulations, as well as exact diagonalization for N=4. Our results show enhanced ferromagnetic correlations in some regions, but apparently no ferromagnetic long-range order. In the half-filled case, our numerical results are consistent with a nonzero critical U. For a non-half-filled band our results suggest that there is no long-range order.