具有电荷配对和Hubbard相互作用的自旋1/2费米子的可积性
Integrability of the spin-1/2 fermions with charge pairing and Hubbard interaction
摘要：
本文研究了一维自旋$\frac{1}{2}$电子模型的精确解，该模型由最近邻三重态对项和在位Hubbard相互作用组成。我们认为，这个模型承认通过映射到一个哈伯德链与虚构的动力学跳跃条款的贝特anterior解决方案。Bethe方程与Lieb和Wu \cite{LW}发现的方程相似，但具有取决于环尺寸的额外扭曲相。我们通过精确对角化和大晶格尺寸下的Bethe方程研究了具有排斥作用的模型的谱。该模型的一个特点是，它是可以定义的电荷间隙为偶数和奇数的晶格位置，都收敛到相同的值在无限大的限制。我们分析了对低位自旋激发的有限尺寸修正，并认为它们等价于自旋- $\frac{1}{2}$各向同性海森堡模型，其边界扭曲取决于晶格宇称。我们提出了经典的统计力学模型，它的传递矩阵与模型的哈密顿量是交换的。为此，我们使用了Shastry \cite{SHA1,SHA2}为哈伯德模型所采用的结构。然而，在我们的例子中，构建块是一个具有特定零权重的自由费米子八顶点模型。
英文摘要：
In this paper we study the exact solution of a one-dimensional model of spin-$\frac{1}{2}$ electrons composed by a nearest-neighbor triplet pairing term and the on-site Hubbard interaction. We argue that this model admits a Bethe ansatz solution through a mapping to a Hubbard chain with imaginary kinetic hopping terms. The Bethe equations are similar to that found by Lieb and Wu \cite{LW} but with additional twist phases which are dependent on the ring size. We have studied the spectrum of the model with repulsive interaction by exact diagonalization and through the Bethe equations for large lattice sizes. One feature of the model is that it is possible to define the charge gap for even and odd lattice sites and both converge to the same value in the infinite size limit. We analyze the finite-size corrections to the low-lying spin excitations and argue that they are equivalent to that of the spin-$\frac{1}{2}$ isotropic Heisenberg model with a boundary twist depending on the lattice parity. We present the classical statistical mechanics model whose transfer matrix commutes with the model Hamiltonian. To this end we have used the construction employed by Shastry \cite{SHA1,SHA2} for the Hubbard model. In our case, however, the building block is a free-fermion eight-vertex model with a particular null weight.
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