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A perturbative and variational approach to quantum lattice Hamiltonians

AuthorsEsteve, J.G.; Sierra, Germán
Issue Date1-Apr-1995
PublisherAmerican Physical Society
CitationPhysical Review B 51: 8928- 8938 (1995)
AbstractWe propose a method to construct the ground state ψ(λ) of local lattice Hamiltonians with the generic form H0+λH1, where λ is a coupling constant and H0 is a Hamiltonian with a nondegenerate ground state ψ0. The method is based on the choice of an exponential ansatz ψ(λ)=exp[U(λ)]ψ0, which is a sort of generalized lattice version of a Jastrow wave function. We combine perturbative and variational techniques to get successive approximations of the operator U(λ). Perturbation theory is used to set up a variational method which in turn produces nonperturbative results. The computation with this kind of ansatz leads us to associate to the original quantum-mechanical problem a statistical-mechanical system defined in the same spatial dimension. In some cases these statistical-mechanical systems turn out to be integrable, which allows us to obtain exact upper bounds to the energy. The general ideas of our method are illustrated in the example of the Ising model in a transverse field. © 1995 The American Physical Society.
Description11 págs.; 2 figs.; 2 tabs.; 4 apps.
Publisher version (URL)https://doi.org/10.1103/PhysRevB.51.8928
Identifiersdoi: 10.1103/PhysRevB.51.8928
issn: 0163-1829
Appears in Collections:(CFMAC-IFF) Artículos
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