Two-dimensional Hubbard model at low-electron density

Osamu Narikiyo, Yasumasa Hasegawa, Hidetoshi Fukuyama

Hidetoshi Fukuyama, Osamu Narikiyo, Yasumasa Hasegawa

The two-dimensional Hubbard model has been studied in the region of low electron density based on the t -matrix approximation. This can take proper account of the singular behaviors of the forward scattering whose importance was indicated by Anderson. By performing first the angular integrations in the irreducible particle-particle correlation function, we can prove analytically that all of the poles of the t -matrix lie on the real axis. Hence the t -matrix and then the self-energy of the retarded Green function, Σ( k , z ), are analytic in the upper half-plane of the energy variable, z . This, together with Im Σ( k F , ε+i δ)∝ε 2 ln |ε|, leads to the conclusion that the electrons described by the two-dimensional Hubbard model are Fermi liquid, at least in the region of low electron density.

Y.-C. Chen, Adriana Moreo, F. Ortolani +2 more

The spin- and density-correlation functions of the two-dimensional Hubbard model at low electronic density 〈n〉 are calculated in the ground state by using the power method, and at finite temperatures by using the quantum Monte Carlo technique. Both approaches produce similar results, which are in close agreement with numerical and high-temperature-expansion results for the two-dimensional t-J model. Using perturbative approximations, we show that the examination of the density-correlation function alone is not enough to support recent claims in the literature that suggested spin and charge separation in the low electronic density regime of the t-J model.

L. B. Ioffe, A. I. Larkin

I. Morgenstern

O Springer-Verlag

The Hubbard model H = - t Zc~,cr, + U Xn~T n~, with N electrons and periodic boundary condition is studied on v-dimensional L~ x .-. x L~ lattices. It is shown that for any value of U there is no ground state with maximal spin (S = N/2) in the following cases: (i) 7/~ (v > 2) at low electron densities; with one hole if t > 0 and L~ is odd for some i; with two holes if t 0 and all the L~ are even. (ii) The bcc lattice at low densities; with two holes if t 0 and all the L~ are even; with 2 ..... 6 holes if L~ = Land t 0 and L is even. (iii) The triangular lattice at densities near 0 and 1 if t > 0; with two holes if t 0; with two holes if t < 0. Some results for the one dimensional model are also presented.