可积开边界条件下的q形变玻色子模型

利用代数Bethe Ansatz方法在可积开边界条件下推广了q形变玻色子模型，得到可积开边界条件下此模型的哈密顿量及其本征方程.该工作可为在更小尺度下研究具有相互作用的玻色子系统提供有效的理论基础. 关键词： 代数Bethe Ansatz q形变玻色子模型')" href="#">q形变玻色子模型 开边界 可积系统     

开边界条件下Fateev-Zamolodchikov模型的潜藏定域规范不变性

在量子反散射方法框架内详细研究了开边界条件下Fateev-Zamolodchikov模型的潜藏定域规范不变性。结果表明,尽管模型Hamiltonian量及其本征矢明显规范相关,但能量本征值和Bethe方程却是规范不变的。 关键词：     

HXXZ模型与量子SUq(2)群的表示

本文利用Bethe Ansatz方法讨论具有特定的边界条件的H_xxz模型与量子SU_q(2)群表示,证明对任意q值,BA态是量子SU_q(2)的最高权态,由此生成量子群的不可约表示,对q=e^ir为单位根,证明Bethe Ansatz方程存在新的解组,利用极限方法,导出|b′>,构造了量子SU_q(2)群的不完全可约表示(Ⅰ型)和不可约表示(Ⅱ型)。 关键词：     

可积开边界条件下XXX-1/2自旋链模型的Gaudin公式

利用量子空间可因式化F算子,在量子反散射的框架内计算出了可积开边界条件下XXX12自旋链模型的Bethe态的标量积和模,得到了用谱参量函数的行列式表达的开边界条件下的Gaudin公式. 关键词： 可积模型 关联函数 开边界     

Osp(1,2)自旋链的潜藏定域规范不变性

在量子反散射框架内研究了Osp（1，2）自旋链的潜藏定域规范不变性．结果表明，该模型允许AbelU（1）规范变换，其能谱在规范变换下保持不变，而本征矢及Bethe ansatz方程明显与规范变换相关． 关键词：     

自旋梯可积模型的研究

通过对自旋梯可积模型的研究,求出该模型的能量本征值和两体散射矩阵.用可积模型中的坐标Bethe Ansatz方法,首先由薛定谔方程求得能量的本征方程.设定波函数的具体形式,求出本征能量,然后利用能量本征方程和波函数的连续性求出两体散射矩阵.求出单粒子、双粒子和N₀个粒子的本征能量,同时求得粒子的两体散射矩阵.自旋梯可积模型的本征能量和两体散射矩阵可通过Bethe Ansatz的方法求得.     

可积开边界条件下的 q 形变玻色子模型

利用代数Bethe Ansatz方法在可积开边界条件下推广了q形变玻色子模型,得到可积开边界条件下此模型的哈密顿量及其本征方程.该工作可为在更小尺度下研究具有相互作用的玻色子系统提供有效的理论基础.     

最一般的超矩阵量子非线性Schr?dinger模型的本征态研究

本文用量子反散射方法讨论了最一般的超矩阵量子非线性Schr?dinger模型的本征态。特别是构造了玻色和费密粒子混合的N粒子束缚态。N粒子的散射态和束缚态的能量分别为∑_j=1^Nλ_j²和Np²-(c²/12)N(N²-1)。 关键词：     

推广t-J模型的坐标Bethe Ansatz方法

利用坐标Bethe Ansatz方法,研究了推广的t—J模型的精确解,导出了两组Bethe Ansatz方程;同时证明了在两体散射问题中的散射矩阵正是三角型的非对称六顶角R矩阵.     

最一般的超矩阵量子非线性Schrdinger模型的本征态研究

本文用量子反散射方法讨论了最一般的超矩阵量子非线性Schrdinger模型的本征态。特别是构造了玻色和费密粒子混合的N粒子束缚态。N粒子的散射态和束缚态的能量分别为     

The six-vertex model eigenvectors as critical limit of the eight-vertex model bethe ansatz

The critical limit of the eight-vertex model eigenvectors obtained by means of the generalized Bethe Ansatz is shown to give the six-vertex eigenvectors as constructed in a previous paper by two of the authors. Furthermore, an explicit mapping is established between these eigenvectors and the usual Bethe Ansatz eigenvectors of the six-vertex model. This allows one to show that the indexv labeling the eight-vertex eigenstates becomes exactly the third component of the total spin in the critical limit.     

Orthogonality and completeness of the Bethe Ansatz eigenstates of the nonlinear Schroedinger model

A rigorous proof is given of the orthogonality and the completeness of the Bethe Ansatz eigenstates of theN-body Hamiltonian of the nonlinear Schroedinger model on a finite interval. The completeness proof is based on ideas of C.N. Yang and C.P. Yang, but their continuity argument at infinite coupling is replaced by operator monotonicity at zero coupling. The orthogonality proof uses the algebraic Bethe Ansatz method or inverse scattering method applied to a lattice approximation introduced by Izergin and Korepin. The latter model is defined in terms of monodromy matrices without writing down an explicit Hamiltonian. It is shown that the eigenfunctions of the transfer matrices for this model converge to the Bethe Ansatz eigenstates of the nonlinear Schroedinger model.     

Existence of Solutions to the Bethe Ansatz Equations for the 1D Hubbard Model: Finite Lattice and Thermodynamic Limit

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 any U>0 to U=∞ 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.     

Drinfel'd Twists and Functional Bethe Ansatz

Using the Functional Bethe Ansatz technique, factorizing Drinfel'd twists for any finite dimensional irreducible representations of the Yangian Y(sl₂) are constructed.     

Novel magnetic properties of the Hubbard chain with an attractive interaction

The magnetic properties of an attractive Hubbard chain are considered. Based on the Bethe Ansatz equations of the problem, exact analytic expressions are derived for the magnetization and susceptibility. These formulae can be evaluated after solving certain derivatives of the Bethe Ansatz equations. These derivative equations are also given. We give the magnetization and susceptibility curves for several values of the interaction-strength and bandfilling. We find that the susceptibility at the onset of magnetization (at the critical field) isfinite for all bandfillings, except for the cases of half filled and empty bands, and in the limit of vanishing interaction. We argue that the finiteness of the initial susceptibility is due to the fermion-like behavior of the bound pairs. We also give the gap (what is equal to the critical field) and the initial susceptibility as functions of the interaction-strength and bandfilling for the cases of nearly half filled and almost empty bands as a function of the interaction, and in the weak coupling limit as a function of the bandfilling. To our knowledge, this is the first Bethe Ansatz calculation for the gap in this latter limit.     

Unitarity of the Knizhnik-Zamolodchikov-Bernard connection and the Bethe Ansatz for the elliptic Hitchin systems

We work out finite-dimensional integral formulae for the scalar product of genus one states of the groupG Chern-Simons theory with insertions of Wilson lines. Assuming convergence of the integrals, we show that unitarity of the elliptic Knizhnik-Zamolodchikov-Bernard connection with respect to the scalar product of CS states is closely related to the Bethe Ansatz for the commuting Hamiltonians building up the connection and quantizing the quadratic Hamiltonians of the elliptic Hitchin system.     

A New Asymmetric Long-Range Model and Algebraic Bethe Ansatz

A new integrable long-range model is derived from a new asymmetric R-matrix recently discussed by Bibikov in relation to a XXZ spin chain in an external magnetic field. The algebraic Bethe Ansatz is used to derive the eigenvalues and equations for the eigen momenta both for the usual and long-range model.     

The Yang-Yang thermodynamic formalism and Large Deviations

The partition function for a one-dimensional system of Bosons with repulsive delta-function interaction is investigated. We prove that if the Bethe Ansatz eigenfunctions form a complete set then the grand canonical pressure is given by the Yang-Yang formula. The proof uses a probabilistic formalism to express the partition function as an expectation with respect to a probability measure on a Banach space of measures; the asymptotic behaviour of the expectation in the thermodynamic limit is determined by the Large Deviation Principle. This method is applicable in situations in which the Hamiltonian can be diagonalised using the Bethe Ansatz.     

The new formulas for the eigenvectors of the Gaudin model in the <Emphasis Type="Italic">so</Emphasis>(5) case

In our recent paper we proposed new formulas for eigenvectors of the Gaudin model in sl(3) case. Similarly in this paper we used the standard Bethe Ansatz method for finding the eigenvectors and the eigenvalues in the so(5) case in an explicit form.