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International Journal of Modern Physics B

FINITE TEMPERATURE RESULTS FROM CONSTRAINED FERMIONIZATION IN THE 2-D SPIN 1/2 HEISENBERG ANTIFERROMAGNET II: FLUCTUATIONS IN THE DIMER PHASES

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

Published Mar 15, 1994• 2 citations
Publisher

Abstract

The constraint of single-site occupancy is implemented in the fermionization of the model, within the saddle point approximation. The columnar and the staggered dimer phases are studied and the contribution of the fluctuations to the zero point energy and the specific heat is analyzed.
DOI
10.1142/s0217979294000300

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Thermal properties of the ordered phase of the spin 1/2 isotropic Heisenberg Antiferromagnet on a d-dimensional hypercubical lattice are studied within the fermionic representation when the constraint of single occupancy condition is taken into account by the method suggested by Popov and Fedotov. Using saddle point approximation in path integral approach we discuss not only the leading order but also the fluctuations around the saddle point at one-loop level. The influence of taking into account the single occupancy condition is discussed at all steps.
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 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.