High-temperature expansions for the strongly correlated Hubbard model in the limit of infinite dimension

We investigate the Hall effect and the magnetoresistance of strongly correlated electron systems using the dynamical mean-field theory. We treat the low- and high-temperature limits analytically and explore some aspects of the intermediate-temperature regime numerically. We observe that a bipartite-lattice condition is responsible for the high-temperature result $\sigma_{xy}\sim 1/T^2$ obtained by various authors, whereas the general behavior is $\sigma_{xy}\sim 1/T$, as for the longitudinal conductivity. We find that Kohler's rule is neither obeyed at high nor at intermediate temperatures.Comment: 9 pages, 7 figures, accepted for publication in Phys. Rev.

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“…This is made possible by the inclusion of diagonal hops t (d) . To leading order in 1/T [26], we find R * H = 6t 2 t (d)…”

Section: The High-temperature Limitmentioning

confidence: 95%

Magnetotransport in the doped Mott insulator

Lange

Kotliar

1999

Phys. Rev. B

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“…Later, Beni et al [8] applied the standard high temperature expansion (a perturbation theory in the hopping constant t) to derive the grand potential of the one-dimensional Hubbard model up to order t 2 . The literature offers many examples of high temperature expansions of the grand canonical partition function for the Hubbard model in d−dimensions for d ≥ 2, some of them up to order β 9 (β = 1 kT ) [9,10,11]. However, all these works refer to some perturbative scheme where one of the characteristic constants of the model (i.e., its parameters) must be much larger than the other ones.…”

Section: Introductionmentioning

confidence: 99%

Analytical results of the one-dimensional Hubbard model in the high-temperature limit

et al. 2001

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We investigate the grand potential of the one-dimensional Hubbard model in the high temperature limit, calculating the coefficients of the high temperature expansion (β-expansion) of this function up to order β 4 by an alternative method. The results derived are analytical and do not involve any perturbation expansion in the hopping constant, being valid for arbitrary density of electrons in the onedimensional model. In the half-filled case, we compare our analytical results for the specific heat and the magnetic susceptibility, in the high-temperature limit, with the ones obtained by Beni et al. and Takahashi's integral equations, showing that the latter result does not take into account the complete energy spectrum of the one-dimensional Hubbard model. The exact integral solution by Jüttner et al. is applied to the determination of the range of validity of our expansion in β in the half-filled case, for several different values of U .

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“…For the Hubbard model with arbitrary U only a fourth-order series has been calculated [7]. In the limit of infinite spatial dimensions Thompson and co-workers [8] derived a tenth-order expansion for the U = °° Hubbard model. For this case Kubo and Tada [9] generated ninth-order expansions for a number of 2D and 3D lattices.…”

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confidence: 99%

Aspects of the phase diagram of the two-dimensionalt-Jmodel

1992

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The phase diagram of the 2D t-J model is investigated using high-temperature expansions. Series for the Heimholtz free energy, the inverse compressibility, the chemical potential, and the uniform spin susceptibility through tenth order are calculated and analyzed. A region of phase separation is found at 7=0 for Jit lying above a line extending from Jit =3.8 at zero filling to Jit = 1.2 at half filling. For very small Jit near half filling where the Nagaoka effect is possible, we find a region of divergent uniform magnetic susceptibility at T-0.

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High-temperature expansions for the strongly correlated Hubbard model in the limit of infinite dimension

Cited by 17 publications

References 27 publications

Magnetotransport in the doped Mott insulator

Magnetotransport in the doped Mott insulator

Analytical results of the one-dimensional Hubbard model in the high-temperature limit

Aspects of the phase diagram of the two-dimensionalt-Jmodel

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