Existence of Solutions to the Bethe Ansatz Equations for the 1D Hubbard Model: Finite Lattice and Thermodynamic Limit
作者： Pedro S. Goldbaum
DOI: 10.1007/S00220-005-1357-Y
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摘要: In this work, we present a proof of the existence real and ordered solutions to generalized Bethe Ansatz equations for one dimensional Hubbard model on finite lattice, with periodic boundary conditions. The continuous set extending from any U>0 U=∞ is also shown. We use continuity property, combined that norm wavefunction obtained not zero, prove solution gives us ground state system, as assumed by Lieb Wu. Lastly, absolute at half-filling, show converges distribution in thermodynamic limit. This limit satisfies integral led Lieb-Wu 1D model.
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Fabian H. L. Essler, Holger Frahm, Frank Göhmann, Andreas Klümper, Vladimir E. Korepin, The one-dimensional Hubbard model odhm. ,(2005) , 10.1017/CBO9780511534843
F. Göhmann, V.E. Korepin, The Hubbard chain: Lieb–Wu equations and norm of the eigenfunctions Physics Letters A. ,vol. 263, pp. 293- 298 ,(1999) , 10.1016/S0375-9601(99)00774-4
Elliott H. Lieb, F.Y. Wu, The one-dimensional Hubbard model: a reminiscence Physica A-statistical Mechanics and Its Applications. ,vol. 321, pp. 1- 27 ,(2003) , 10.1016/S0378-4371(02)01785-5
F Woynarovich, Excitations with complex wavenumbers in a Hubbard chain. II. States with several pairs of complex wavenumbers Journal of Physics C: Solid State Physics. ,vol. 15, pp. 97- 109 ,(1982) , 10.1088/0022-3719/15/1/008
Elliott H. Lieb, F. Y. Wu, Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension Physical Review Letters. ,vol. 20, pp. 1445- 1448 ,(1968) , 10.1103/PHYSREVLETT.20.1445
C. N. Yang, Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction Physical Review Letters. ,vol. 19, pp. 1312- 1315 ,(1967) , 10.1103/PHYSREVLETT.19.1312
Kareljan Schoutens, Vladimir E. Korepin, Fabian H.L. Eβler, Completeness of the SO(4) extended Bethe ansatz for the one-dimensional Hubbard model Nuclear Physics. ,vol. 384, pp. 431- 458 ,(1992) , 10.1016/0550-3213(92)90575-V
Daniel H. Gottlieb, Geetha Samaranayake, The Index of Discontinuous Vector Fields The New York Journal of Mathematics [electronic only]. ,vol. 1, pp. 130- 148 ,(1995)
ELECTRON CORRELATIONS IN NARROW ENERGY BANDS Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 276, pp. 238- 257 ,(1963) , 10.1098/RSPA.1963.0204
C. N. Yang, C. P. Yang, One-Dimensional Chain of Anisotropic Spin-Spin Interactions. I. Proof of Bethe's Hypothesis for Ground State in a Finite System Physical Review. ,vol. 150, pp. 321- 327 ,(1966) , 10.1103/PHYSREV.150.321