A symmetry-projected variational approach to the 1-dimensional Hubbard-model

Abstract

We apply a variational method devised for the nuclear many--body problem to the 1-dimensional Hubbard--model with nearest neighbor hopping and periodic boundary conditions. The test wave function consist for each state out of a single Hartree--Fock determinant mixing all the sites (or momenta) as well as the spin--projections of the electrons. Total spin and linear momentum are restored by projection methods before the variation. It is demonstrated that this approach reproduces the results of exact diagonalisations for half--filled N=12 and N=14 lattices not only for the energies and occupation numbers of the ground but also of the lowest excited states rather well. Furthermore, a system of 10 electrons in a N=12 lattice is investigated and, finally, a N=30 lattice is studied. In addition to energies and occupation numbers we present the spectral functions computed with the help of the symmetry--projected wave functions, too. Also here nice agreement with the exact results (where available) is reached.

arXiv comment24 pages, 16 figures

References in corpus (5)

• Quantum Monte Carlo Calculations of Light Nuclei
• Spectral function of the one-dimensional Hubbard model away from half filling
• Spectral functions of the 1D Hubbard model in the U -> \infty limit: How to use the factorized wave-function
• Quantum-number projection in the path-integral renormalization group method
• Correlations in Nuclei: Self-Consistent Treatment and the BAGEL Approach

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• Projected Quasiparticle Theory for Molecular Electronic Structure
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• Symmetry-projected Wave Functions in Quantum Monte Carlo Calculations
• Multi-reference symmetry-projected variational approaches for ground and excited states of the one-dimensional Hubbard model
• Symmetry-projected variational approach for ground and excited states of the two-dimensional Hubbard model
• Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants
• N-electron Slater determinants from non-unitary canonical transformations of fermion operators
• Topological flat bands in optical checkerboard-like lattices
• Multi-reference symmetry-projected variational approximation for the ground state of the doped one-dimensional Hubbard model
• Ground States of Heisenberg Spin Clusters from Projected Hartree-Fock Theory
• Exact Ground State of Strongly Correlated Electron Systems from Symmetry-Entangled Wave-Functions
• Ground states of Heisenberg spin clusters from a cluster-based projected Hartree-Fock approach
• Projective spin adaptation for the exact diagonalization of isotropic spin clusters