V. Fomin, L. Frappat, E. Ragoucy
We compute the Bethe equations of generalized Hubbard models, and study their thermodynamical limit. We argue how they can be connected to the ones found in the context of AdS/CFT correspondence, in particular with the so-called dressing phase problem. We also show how the models can be interpreted, in condensed matter physics, as integrable multi-leg Hubbard models.
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We compute the eigenfunctions, energies and Bethe equations for a class of generalized integrable Hubbard models based on gl(n|m)\oplus gl(2) superalgebras. The Bethe equations appear to be similar to the Hubbard model ones, up to a phase due to the integration of a subset of `simple' Bethe equations. We discuss relations with AdS/CFT correspondence, and with condensed matter physics.
The one-dimensional Hubbard model with arbitrary boundary magnetic fields is solved exactly via the Bethe ansatz methods. With the coordinate Bethe ansatz in the charge sector, the second eigenvalue problem associated with the spin sector is constructed. It is shown that the second eigenvalue problem can be transformed into that of the inhomogeneous XXX spin chain with arbitrary boundary fields which can be solved via the off-diagonal Bethe ansatz method.
We calculate explicitly the Bethe vectors states by the algebraic Bethe ansatz method with the $gl(2)$-invariant $R$-matrix for the two-site Bose-Hubbard model. Using a binomial expansion of the n-th power of a sum of two operators we get and solve a recursion equation. We calculate the scalar product and the norm of the Bethe vectors states. The form factors of the imbalance current operator are also computed.
Algebraic Bethe ansatz approach for the one-dimensional Hubbard model
本文用量子逆散射方法给出了一维哈伯德模型的代数Bethe近似解。开发的方法是基于一组新的交换关系，它编码一个隐藏的对称性的6顶点类型。
Bosonization Based on Bethe Ansatz Equations and Spin-Charge Separation in the Hubbard Model with Finite U
我们开发了一个玻色化方法的基础上的一维模型的贝特anonymous方程。精确可解模型在低能极限下的算子形式提供了一种计算渐近关联函数的系统方法。作为有和无内自由度的例子，分别考虑了Calogero-Sutherland（C-S）模型和排斥哈伯德模型。我们证实了C-S模型的低能行为是由两类c=1的共形场论控制的，这取决于C-S相互作用是玻色子间的还是费米子间的.对于哈伯德模型，我们给出了低能下任意U>0的电荷自旋分离。系统的低能行为由两个独立的维拉索罗代数的（半）直积来描述，其中c=1。
I introduce a new parametrization of a bosonic Lax operator for the algebraic Bethe ansatz method with the $gl(2)$-invariant $R$-matrix and use it to present the exact solution of a generalized two-sites Bose-Hubbard model with asymmetric tunnelling. In the no interaction limit I show that the Bethe ansatz equations can be written as a $S^{N-1}$ sphere, where $N$ is the total number of atoms in the condensate.
Inspired by recent results in the context of AdS/CFT integrability, we reconsider the Thermodynamic Bethe Ansatz equations describing the 1D fermionic Hubbard model at finite temperature. We prove that the infinite set of TBA equations are equivalent to a simple nonlinear Riemann-Hilbert problem for a finite number of unknown functions. The latter can be transformed into a set of three coupled nonlinear integral equations defined over a finite support, which can be easily solved numerically. We discuss the emergence of an exact Bethe Ansatz and the link between the TBA approach and the results…
Bosonization and correlators of the one-dimensional Hubbard model
本研究针对一维Hubbard模型，给出了有限与无穷排斥势下Luttinger液体关系的简洁推导，利用玻色化技术计算关联函数渐近行为，并通过Bethe Ansatz参数实现临界指数的清晰物理表述。
Algebraic Bethe ansatz for the gl(1|2) generalized model and Lieb-Wu equations
我们求解了gl（1| 2）代数Bethe分析的广义模型。由此产生的特征值的传递矩阵和贝特方程依赖于三个复杂的功能，称为参数的广义模型。通过适当地调整参数，我们得到了超对称t-J模型、哈伯德模型和具有δ相互作用的电子的Yang模型的Bethe不等式.这意味着这些（和许多其他）模型的Bethe不等式方程可以从一个共同的代数源获得，即从由gl（1）生成的Yang-Baxter代数获得|2）不变R-矩阵。
The Hubbard quantum wire
通过引入量子线的边界条件，利用Bethe近似精确求解了哈伯德模型。明确定义了束缚态的波函数，精确地得到了谱的久期方程。在热力学极限下研究了基态和低激发态激发态。明确地得到了强耦合极限下的基态能量，并与周期边界条件下的结果进行了比较。
The nonadiabatic quantum tunneling picture, which may be called the many-body Schwinger-Landau-Zener mechanism, for the dielectric breakdown of Mott insulators in strong electric fields is studied in the one-dimensional Hubbard model. The tunneling probability is calculated by a metod due to Dykhne-Davis-Pechukas with an analytical continuation of the Bethe-ansatz solution for excited states to a non-Hermitian case. A remarkable agreement with the time-dependent density matrix renormalization group result is obtained.
Hubbard's Adventures in ${\cal N}=4$ SYM-land? Some non-perturbative considerations on finite length operators
由于半填充时的Hubbard能量被认为是在强耦合下再现了平面$ {\cal N}=4$ SYM的SU（2）扇区中的维数的全圈展开的一部分，为此，我们利用二维统计场论中的有效和众所周知的思想，将Bethe Anasterian方程转化为两个耦合的非线性积分方程（NLIE）.我们把我们的注意力集中在固定裸维或长度的最高反常维数$L$，分析了这种方法的许多优点，提取准确的行为变化的长度和t Hooft耦合，$λ$。例如，我们将表明，大$L$（渐近）的扩展是完全复制其类似物在BDS贝特Angloman，虽然确切的表达明显不同于BDS之一（非解析条款）。对$L$和$λ$以不同顺序执行限制也受到严格控制。最后，非线性弹性理论的数值积分的精度与其他看起来更精确的理论一样令人印象深刻。
Scaling limit of the one-dimensional attractive Hubbard model: The half-filled band case
研究了宏观半满Hubbard链高阶Bethe Answer（HLBA）方程的标度极限。这些方程实际上解耦成三个不相交的集合，这些集合又是BA型的，并且对应于三种不同类型的修饰粒子（一个有质量的和两个无质量的）的长期方程。有限尺寸修正和谱的精细结构表明，无质量扇形对应于一个具有中心荷c=1和高斯反常维数的共形场。计算了零温自由能，发现与SU（2）手征Gross-Neveu（CGN）模型的微扰计算结果完全一致。
Exactly integrable family of generalized Hubbard models with twisted Yangian symmetry
本文考虑了一个具有受控跳跃的强关联电子系统，它与最近提出的作为高T_c超导体候选者的广义哈伯德模型一致。该模型以及一类这样的系统被证明是完全可积的明确的量子R-矩阵和Lax算子。尽管Bethe模型的解很新颖，但最终的结果与标准哈伯德模型的结果相差不大。然而，该模型的对称性被改变为最近发现的扭曲的杨氏对称性。
The Bethe-Salpeter equation plays a crucial role in understanding the physics of correlated fermions, relating to optical excitations in solids as well as resonances in high-energy physics. Yet, it is notoriously difficult to control numerically, typically requiring an effort that scales polynomially with energy scales and accuracy. This puts many interesting systems out of computational reach. Using the intermediate representation and sparse modelling for two-particle objects on the Matsubara axis, we develop an algorithm that solves the Bethe-Salpeter equation in $O(L^8)$ time with $O(L^4)$ …
String hypothesis for the AdS_5 x S^5 mirror
我们讨论了在AdS_5 × S^5背景下，由光锥规范固定的弦论通过双芯转动得到的镜像理论的热力学极限中起作用的态。我们分析了镜像理论的Bethe-Yang方程，并提出了弦假设。我们表明，在热力学极限解的Bethe-Yang方程安排成贝特字符串配置类似的哈伯德模型中出现的。我们还导出了一组描述镜像理论的束缚态和Bethe弦组态的方程。
Thermodynamics of Non-Relativistic Scattering Theory
本文利用热力学Bethe近似，利用Eßler和Korepin提出的$S$ -矩阵，研究了一维哈伯德模型低能激发的非相对论散射理论.这个模型可以用两种激发态来描述，holon和spinon，作为渐近态。在吸引态下，自旋子是有质量的，而合子是无质量的。情况与排斥耦合相反。我们导出了哈伯德模型的中心荷在IR极限为$c=1$，而在UV极限为零.贡献是由于无质量的自由度，即合子的吸引制度，和有质量的模式完全重叠。这一结果与基于格点Bethe变换计算的各种已知结果是一致的。我们的结果使得有可能使用的$S$ -矩阵的激励计算更有趣的数量，如关联函数。
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