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Bulk Property on Cayley Tree with Smooth Boundary Condition
Hiro-Aki Hotta
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We study a nearest-neighbor hopping model on the Cayley tree under the smooth boundary condition with the modulation function fₛ=sin²[πs/(2M+1)], where s is a distance from the central site, and M is the number of shells on the tree. As a result of this smoothing, the particle density in the ground state becomes nearly uniform in the bulk region even when M is relatively small. We compare the calculated particle density at the center with exact result on the Bethe lattice, and they show a good agreement. The calculated bond energy at the center also agrees with that on the Bethe lattice.
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