Optimized t-expansion method for the Rabi Hamiltonian |
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Authors: | Igor Travěnec Ladislav Šamaj |
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Institution: | Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 845 11 Bratislava, Slovakia |
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Abstract: | A polemic arose recently about the applicability of the t-expansion method to the calculation of the ground state energy E0 of the Rabi model. For specific choices of the trial function and very large number of involved connected moments, the t-expansion results are rather poor and exhibit considerable oscillations. In this Letter, we formulate the t-expansion method for trial functions containing two free parameters which capture two exactly solvable limits of the Rabi Hamiltonian. At each order of the t-series, E0 is assumed to be stationary with respect to the free parameters. A high accuracy of E0 estimates is achieved for small numbers (5 or 6) of involved connected moments, the relative error being smaller than 10−4 (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 E1, with the relative error smaller than 10−2 (1%). |
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Keywords: | Rabi Hamiltonian Connected moments t-expansion method Ground state Variational trial function |
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