Optimized t-expansion method for the Rabi Hamiltonian
arXiv:1107.4479 · doi:10.1016/j.physleta.2011.09.051
Abstract
A polemic arose recently about the applicability of the -expansion method to the calculation of the ground state energy of the Rabi model. For specific choices of the trial function and very large number of involved connected moments, the -expansion results are rather poor and exhibit considerable oscillations. In this letter, we formulate the -expansion method for trial functions containing two free parameters which capture two exactly solvable limits of the Rabi Hamiltonian. At each order of the -series, is assumed to be stationary with respect to the free parameters. A high accuracy of estimates is achieved for small numbers (5 or 6) of involved connected moments, the relative error being smaller than (0.01%) within the whole parameter space of the Rabi Hamiltonian. A special symmetrization of the trial function enables us to calculate also the first excited energy , with the relative error smaller than (1%).