Existence of Solutions to the Bethe Ansatz Equations for the 1D Hubbard Model: Finite Lattice and Thermodynamic Limit
Existence of Solutions to the Bethe Ansatz Equations for the 1D Hubbard Model: Finite Lattice and Thermodynamic Limit
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一维哈伯德模型 Bethe Ansatz 方程解的存在性：有限格和热力学极限
DOI：
10.1007/s00220-005-1357-y
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
Pedro S. Goldbaum
中科院分区：
文献类型：
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作者：
Pedro S. Goldbaum
本文证明了有限格点上一维Hubbard模型的广义Bethe Answer方程在周期边界条件下存在真实的解和有序解.还证明了从任意U>0到U =∞的连续解集的存在性。我们使用这种连续性的性质，结合证明，与广义Bethe Answer得到的波函数的范数不为零，证明该解决方案给我们的有限系统的基态，由Lieb和吴假设。最后，对于绝对基态在半填充，我们表明，解决方案收敛到一个分布的热力学极限。这个极限分布满足导致1D Hubbard模型的Lieb-Wu解的积分方程。
In this work, we present a proof of the existence of real and ordered solutions to the generalized Bethe Ansatz equations for the one dimensional Hubbard model on a finite lattice, with periodic boundary conditions. The existence of a continuous set of solutions extending from anyU>0 toU=∞ is also shown. We use this continuity property, combined with the proof that the norm of the wavefunction obtained with the generalized Bethe Ansatz is not zero, to prove that the solution gives us the ground state of the finite system, as assumed by Lieb and Wu. Lastly, for the absolute ground state at half-filling, we show that the solution converges to a distribution in the thermodynamic limit. This limit distribution satisfies the integral equations that led to the Lieb-Wu solution of the 1D Hubbard model.