GENERALIZED WIGNER LATTICES AS A RIEMANN SOLID: FRACTALS IN THE HURWITZ ZETA FUNCTION
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We study the ground state configuration and the excitation energy gaps in the strong coupling limit of the extended Hubbard model with a long-range interaction in one dimension. As proved by Hubbard and Pokrovsky and Uimin, the ground state configuration is quasiperiodic and as proved by Bak and Bruinsma, the excitation energy has a finite gap which forms a devil's stair as a function of the density of particles in the system. We show that the quasiperiodicity and the fractal nature of the excitation energy come from the nature of the long-range interaction that is related to the fractal nature of the Hurwitz Zeta function and the Riemann Zeta function.
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1971 ◽
Vol 55
(11)
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pp. 5421-5422
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1974 ◽
Vol 24
(4)
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pp. 457-460
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1997 ◽
Vol 106
(12)
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pp. 5049-5061
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2018 ◽
Vol 10
(1)
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pp. 01022-1-01022-5
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2021 ◽
Vol 1762
(1)
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pp. 012016
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