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International Journal of Modern Physics B

SINGLE SITE-OCCUPANCY CONSTRAINT FOR THE HUBBARD MODEL AT FINITE TEMPERATURE

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

Published Aug 15, 1993• 5 citations
Publisher

Abstract

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.

DOI
10.1142/s0217979293003231

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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 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.
Slave bosons are commonly introduced in order to implement an infinite Hubbard U by means of a local constraint. The usual starting point for investigations within this scheme is a mean-field theory in which the constraint is taken to be global. This approximate treatment of the constraint is studied in the context of a two-band Hubbard model, and it is shown that (i) the ground state has a significant number of doubly occupied sites, despite the infinite on-site repulsion in the original model, and (ii) there is an unphysical tendency for pairing. However, it is found that if the local constraint is retained for the insulator at half filling, then mean-field theory gives the correct result that the double occupancy is zero.
We present the exact solution of the one-dimensional extended Hubbard model in the atomic limit within the Green's function and equations of motion formalism. We provide a comprehensive and systematic analysis of the model by considering all the relevant response and correlation functions as well as thermodynamic quantities in the whole parameters space. At zero temperature we identify four phases in the plane (U,n) ( U is the on-site potential and n is the filling) and relative phase transitions as well as different types of charge ordering. These features are endorsed by investigating at T=0 the chemical potential and pertinent local correlators, the particle and double occupancy correlation functions, the entropy, and by studying the behavior in the limit T-->0 of the charge and spin susceptibilities. A detailed study of the thermodynamic quantities is also presented at finite temperature. This study evidences that a finite-range order persists for a wide range of the temperature, as shown by the behavior of the correlation functions and by the two-peak structure exhibited by the charge susceptibility and by the entropy. Moreover, the equations of motion formalism, together with the use of composite operators, allows us to exactly determine the set of elementary excitations. As a result, the density of states can be determined and a detailed analysis of the specific heat allows for identifying the excitations and for ascribing its two-peak structure to a redistribution of the charge density.