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Czechoslovak Journal of Physics

On the symmetries of the Hubbard model: application to finite-size clusters

Mario Cuoco, Canio Noce, Alfonso Romano

Published Apr 1, 1996• 2 citations
Publisher
DOI
10.1007/bf02570929

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With the projector quantum Monte Carlo algorithm and the stochastic diagonalization it is possible to calculate the ground state of the Hubbard model for small finite clusters. Nevertheless the usual finite size scaling of the Hubbard model has problems of deducing the behavior of the infinite system correctly from the numerical data of small system sizes. Therefore we study the finite size scaling of the superconducting correlation functions in superconducting BCS-reduced Hubbard models to analyze the finite size behavior in small finite clusters. The ground state of the BCS-reduced Hubbard models is calculated with the stochastic diagonalization without any approximations. As result of these analyses we propose a new finite size scaling ansatz for the Hubbard model, which is able describe the finite size effects in a consistent way taking the corrections to scaling into account, which are dominant for weak interaction strength and small clusters. With this new finite size scaling ansatz it is possible to give evidence for superconductivity for all interaction strengths for both the attractive tt'-Hubbard model (with s-wave symmetry) and the repulsive tt'-Hubbard model (with dx2-y2-wave symmetry).
We present a method for the simultaneous implementation of the spin symmetry, the pseudospin symmetry and the translational invariance in models for correlated electron systems on finite-size clusters. The application of this method leads to a significative reduction of the size of the Hamiltonian matrix blocks, thus considerably simplifying the diagonalization procedure. We illustrate the method solving exactly the Hubbard model on a 8-site chain in the Hilbert subspaces labelled by the eigenvalues of the spin, the pseudospin and the momentum operators. Some relevant thermodynamical quantities, such as the specific heat and the static magnetic susceptibility, are then evaluated and a brief discussion on the tendency of the model to exhibit ferromagnetism is also presented.