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Physical review. B, Condensed matter

Saddle-point finite-temperature results for the infinite-UHubbard model at half filling

Mario Di Stasio, Elisa Ercolessi, G. Morandi, A. Tagliacozzo, F. Ventriglia

Published Jan 15, 1992• 8 citations
Publisher

Abstract

We implement the constraint of no-double-site occupancy exactly, in the spin-1/2 Hubbard-Heisenberg model at half filling. The staggered Peierls and the flux phase are again found to be saddle points for the effective action, also at finite temperature. Their mean-field critical temperatures are higher when the accuracy restriction is taken into account. Gaussian fluctuations of the auxiliary field are reasonably small for a large temperature range, but have to be necessarily included, when extending the free energy to finite temperatures.

DOI
10.1103/physrevb.45.1939

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We implement the constraint of no-double-site occupancy exactly, in the spin-1/2 Hubbard-Heisenberg model at half filling. The staggered Peierls and the flux phase are again found to be saddle points for the effective action, also at finite temperature. Their mean-field critical temperatures are higher when the accuracy restriction is taken into account. Gaussian fluctuations of the auxiliary field are reasonably small for a large temperature range, but have to be necessarily included, when extending the free energy to finite temperatures.
We show how it is possible to include the constraint of single site-occupancy in the large U limit of the Hubbard model at half-filling by means of a local chemical potential. The formalism which is in principle exact allows for finite temperature mean field results satisfying the constraint within 10%. The method is here applied to the dimerized phase and the commensurate flux phase which are still found as local saddle points of the action. The symmetry properties of these actions have been studied. One loop static corrections have been added to obtain an effective free energy and an estimate of the specific heat. In the limit of zero temperature our results reproduce those of the conventional mean field theory of these phases, because quantum fluctuations have not been included. We find that the temperature destabilizes the flux phase more than it does with the dimer phase, especially due to the constraint, which does not suppress phase fluctuating modes, provided the flux is conserved.
We have calculated the ground-state energy and the fluctuation contribution to the free-energy for the Hubbard model at half filling. We have used a gauge that leads to the Hartree-Fock solution in the saddle-point approximation. The mean-field ground-state energy calculated here agrees with the results obtained by Dagotto et al. [Phys. Rev. B 45, 10 741 (1992)] with use of the exact-diagonalization techniques on a 4\ifmmode\times\else\texttimes\fi{}4 site cluster. In the large-U limit, the ground-state energy per site is obtained as Eg{\mathit{E}}_{\mathit{g}}Eg​/N=-U/4-J+O(J2{\mathit{J}}^{2}J2/U). The fluctuation contribution to the free-energy was found to have a stronger temperature and U dependence than the mean-field contribution, and to play a dominant role for strongly correlated systems.