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Zeitschrift für Physik D Atoms Molecules and Clusters

The Hubbard model for small clusters

J. Callaway, D. P. Chen, R. Tang

Published Mar 1, 1986• 37 citations
Publisher
DOI
10.1007/bf01442352

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The Variational cluster approximation (VCA) is an approximate method for finding properties the Hubbard model, the basic model used in the study of strongly correlated electron systems. Such systems include, for instance, high-temperature and organic superconductors.The method involves solving exactly the Hubbard model on a small cluster of lattice sites, after adding fields that represent the effect of the cluster's environment. We present an outline of the method and describe its implementation. In particular, we show how to efficiently carry frequency-wavevector integrals that are central to the method.

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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).
The Hubbard model for small size clusters is investigated.Using direct diagonalization of the small cluster Hamiltonian, electronic, magnetic and spin susceptibilities are calculated and their behavior at low temperature is investigated.The temperature behavior of susceptibilities for twoand three-site clusters is investigated for both center and edge of the Brillouin zone.If at the given concentration the ground state is polarized, the susceptibilities diverge following the Curie law and the system is transformed into the magnetically ordered state at T = 0.
The Variational cluster approximation (VCA) is an approximate method for finding properties the Hubbard model, the basic model used in the study of strongly correlated electron systems. Such systems include, for instance, high-temperature and organic superconductors.The method involves solving exactly the Hubbard model on a small cluster of lattice sites, after adding fields that represent the effect of the cluster's environment. We present an outline of the method and describe its implementation. In particular, we show how to efficiently carry frequency-wavevector integrals that are central to the method.