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Physics Letters A

Calculation of tunnel splitting in a biaxial spin particle without instanton technique

Bin Zhou, Liang Jiu-Qing, Fu‐Cho Pu

Published Dec 1, 2000• 1 citation
Publisher
DOI
10.1016/s0375-9601(00)00744-1

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We present the calculation and comparison of tunnel splitting at excited levels of biaxial spin models by various methods, including the generalized instanton method, the generalized path integral method for coherent spin states, the perturbation method and the exact method by numerical diagonalization of the Hamiltonian. It is found that, for integer spin with spin number around 10, tunnel splitting predicted by the generalized path integral for coherent spin states is about 10 − n times of the exact numerical result for the n th excited level, while the ratio of the results of the perturbation method and the exact numerical method diverges in the large spin limit. We thus conclude that the generalized instanton method is the best approximate way for calculating tunnel splitting in spin models.
A consistent theory of the ground-state energy and its splitting due to the process of tunnelling for the Lipkin - Meshkov - Glick (LMG) model is presented. We calculate accurately the trivial and the instanton saddle-point contributions to the functional integral for the partition function of the model, in terms of the spin coherent states. We show that such a calculation has to be performed very accurately taking into account the discrete nature of the functional integral. This accurate consideration leads to the replacement of the magnitude of the spin s by s + 1/2, in the formula for the ground-state splitting obtained by a naive continuous method. We compare the numerical calculation of the ground-state energy and the splitting due to tunnelling with the results obtained by the quasiclassical method and obtain excellent agreement.