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Explicit Solutions of the Bethe Ansatz Equations for Bloch Electrons in a Magnetic Field
初貝, 安弘
Hatsugai, Yasuhiro
Kohmoto, Mahito
Wu, Yong-Shi
©1994 The American Physical Society
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For Bloch electrons in a magnetic field, explicit solutions are obtained at the center of the spectrum for the Bethe ansatz equations of Wiegmann and Zabrodin. When the magnetic flux per plaquette is 1 / Q with Q an odd integer, distribution of the roots of the Bethe ansatz equation is uniform except at two points on the unit circle in the complex plane. For the semiclassical limit Q→∞, the wave function is
ψ(x)
2=(2 / sin πx), which is critical and unnormalizable. For the golden-mean flux, the distribution of roots has exact self-similarity and the distribution function is nowhere differentiable. The corresponding wave function also shows a clear self-similar structure.
The American Physical Society
1994-08
eng
journal article
http://hdl.handle.net/2241/100822
https://tsukuba.repo.nii.ac.jp/records/16920
10.1103/PhysRevLett.73.1134
0031-9007
AA00773679
Physical review letters
73
8
1134
1137
https://tsukuba.repo.nii.ac.jp/record/16920/files/PRL_73-8.pdf
application/pdf
1.2 MB
2013-12-19