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arXiv:cond-mat/9807402

Comment on "Symmetry properties of magnetization in the Hubbard model at finite temperature"

Adolfo Avella, Francesco Paolo Mancini, D. Villani

Published Jul 30, 1998• 0 citations
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Abstract

The results of G. Su and M. Suzuki [Phys. Rev. B 54, 8291 (1996); ibidem 57, 13367 (1998)] for the spin and pseudo-spin symmetry properties of the Hubbard model are reexamined. We point out that the exact relations they have found are valid down to zero temperature and that their solutions for both spin and pseudo-spin correlation functions are incorrect.

DOI
10.48550/arxiv.cond-mat/9807402

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Reply to "Comment on 'Symmetry properties of magnetization in the Hubbard model at finite temperature'"

Gang Su, Masuo Suzuki

This paper has been withdrawn.

arXiv:cond-mat/9808011•Aug 3, 1998•0 citations
The results of G. Su and M. Suzuki [Phys. Rev. B 54, 8291 (1996); ibidem 57, 13367 (1998)] for the spin and pseudo-spin symmetry properties of the Hubbard model are reexamined. We point out that the exact relations they have found are valid down to zero temperature and that their solutions for both spin and pseudo-spin correlation functions are incorrect.
By making use of some symmetry properties of the relevant Hamiltonian, two fundamental relations between the ferromagnetic magnetization and a spin correlation function are derived for the d(=1,2,3)d(=1,2,3)d(=1,2,3)-dimensional Hubbard model at finite temperatures. These can be viewed as a kind of Ward-Takahashi identity. The properties of the magnetization as a function of the applied field are discussed. The results thus obtained hold true for both repulsive and attractive on-site Coulomb interactions, and for arbitrary electron fillings.
As an extension of our previous rigorous investigation on the spin correlations in the ground states of the half-filled Hubbard model and the periodic Anderson model [G. S. Tian, Phys. Rev. B 50, 6246 (1994)], in the present paper we study the behavior of these correlation functions at finite temperature. We show rigorously that, at any $T\ensuremath{\ne}0,$ the predominant spin correlations in these systems are antiferromagnetic. Furthermore, based on this result, we also show that a quasi-one (or two)-dimensional itinerant electron ferrimagnet must have a gapless branch of ferromagnetic excitations. This conclusion is consistent with the previous results derived by the spin-wave theory.
The observed magnetic spin susceptibility of high-temperature superconductors such as ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Srx{\mathrm{Sr}}_{\mathit{x}}Srx​CuO4{\mathrm{CuO}}_{4}CuO4​ increases when x increases from zero, i.e., as one dopes away from half-filling. Recent Monte Carlo simulations of A. Moreo [Phys. Rev. B 48, 3380 (1993)] suggest that this behavior can be reproduced by the two-dimensional Hubbard model only at large coupling, namely, U/t of order 10. Using longer runs, our Monte Carlo simulations show that the same behavior as for U/t=10 is obtained even in the intermediate coupling regime (U/t=4), as long as the temperature is low enough (T=t/6) that strong antiferromagnetic correlations are building up at half-filling. These results are consistent with the fact that in two dimensions, the generalized random phase approximation should fail in the parameter range where it predicts a magnetic phase transition.
We present an approach to the magnetic properties of the half-filled Hubbard model, based on an approximate mapping of its low-energy transverse spin excitations on to those of an effective underlying Heisenberg model, but with effective spin interactions which are self-consistently determined and not confined solely to nearest-neighbor couplings. The mapping is exact in strong-coupling and is found to be accurate over a very wide range of interaction strengths, down to weak coupling. At zero temperature, it permits ready evaluation at finite U of the one-loop effects of zero-point spin fluctuations on, e.g., the sublattice magnetization. At finite temperatures, thermodynamic properties of the system in the thermal paramagnet are studied via a physically transparent Onsager reaction field approach, which amounts to a self-consistent treatment of paramagnetic spin correlations. This is central not only in recovering the correct dimensionality dependence of antiferromagnetic long-ranged order, but also for the d=3 case of primary interest here yields a N\'eel temperature in close agreement with known strong- and weak-coupling limits. Spin correlation functions and magnetic susceptibilities also show very good agreement with quantum Monte Carlo calculations over an appreciable temperature range in which the low-lying transverse spin excitations are thermally dominant. \textcopyright{} 1996 The American Physical Society.