Using the eigenfunctional method, we derive general functional expressions of the partition function and electron Green's function of the $D$ -dimensional Hubbard model for zero and finite temperatures, in which the sign problem of fermions is avoided. These expressions can be calculated by solving the equation of a phase field and taking the functional average over a Lagrange multiplier field, while for some special cases they can be solved exactly. Moreover, we compare our results with the exact solution of the dynamical mean-field theory in the infinite-dimension limit.Using the eigenfunctional method, we derive general functional expressions of the partition function and electron Green's function of the $D$-dimensional Hubbard model for zero and finite temperatures, in which the sign problem of fermions is avoided. These expressions can be calculated by solving the equation of a phase field and taking the functional average over a Lagrange multiplier field, while for some special cases they can be solved exactly. Moreover, we compare our results with the exact solution of the dynamical mean-field theory in the infinite-dimension limit.

Physical Review BAug 24, 20051 citation

Partition functional and thermodynamic properties of the infinite-dimensional Hubbard model

Y. M. Li, N. d’Ambrumenil

An approximate partition functional is derived for the infinite-dimensional Hubbard model. This functional naturally includes the exact solution of the Falicov-Kimball model as a special case, and is exact in the uncorrelated and atomic limits. It explicitly keeps spin symmetry. For the case of the Lorentzian density of states, we find that the Luttinger theorem is satisfied at zero temperature. The susceptibility crosses over smoothly from that expected for an uncorrelated state with antiferromagnetic fluctuations at high temperature to a correlated state at low temperature via a Kondo-type anomaly at a characteristic temperature ${\mathit{T}}^{\mathrm{*}}$ . We attribute this anomaly to the appearance of the Hubbard pseudogap. The specific heat also shows a peak near ${\mathit{T}}^{\mathrm{*}}$ . The resistivity goes to zero at zero temperature, in contrast to other approximations, rises sharply around ${\mathit{T}}^{\mathrm{*}}$ , and has a rough linear temperature dependence above ${\mathit{T}}^{\mathrm{*}}$ .An approximate partition functional is derived for the infinite-dimensional Hubbard model. This functional naturally includes the exact solution of the Falicov-Kimball model as a special case, and is exact in the uncorrelated and atomic limits. It explicitly keeps spin symmetry. For the case of the Lorentzian density of states, we find that the Luttinger theorem is satisfied at zero temperature. The susceptibility crosses over smoothly from that expected for an uncorrelated state with antiferromagnetic fluctuations at high temperature to a correlated state at low temperature via a Kondo-type anomaly at a characteristic temperature ${\mathit{T}}^{\mathrm{*}}$. We attribute this anomaly to the appearance of the Hubbard pseudogap. The specific heat also shows a peak near ${\mathit{T}}^{\mathrm{*}}$. The resistivity goes to zero at zero temperature, in contrast to other approximations, rises sharply around ${\mathit{T}}^{\mathrm{*}}$, and has a rough linear temperature dependence above ${\mathit{T}}^{\mathrm{*}}$.

arXiv:cond-mat/9401017Physical review. B, Condensed matterMar 1, 19944 citations

Using the eigenfunctional method, we derive general functional expressions of the partition function and electron Green's function of the

D

-dimensional Hubbard model for zero and finite temperatures, in which the sign problem of fermions is avoided. These expressions can be calculated by solving the equation of a phase field and taking the functional average over a Lagrange multiplier field, while for some special cases they can be solved exactly. Moreover, we compare our results with the exact solution of the dynamical mean-field theory in the infinite-dimension limit.

{\mathit{T}}^{\mathrm{*}}

. We attribute this anomaly to the appearance of the Hubbard pseudogap. The specific heat also shows a peak near

{\mathit{T}}^{\mathrm{*}}

. The resistivity goes to zero at zero temperature, in contrast to other approximations, rises sharply around

{\mathit{T}}^{\mathrm{*}}

, and has a rough linear temperature dependence above

{\mathit{T}}^{\mathrm{*}}