Integrable quantum spin chains and their classical continuous counterparts
Jean Avan, Anastasia Doikou, Konstadinos Sfetsos
给出了原型可积量子自旋链的某些经典连续长波极限，并定义了相应的经典连续Lax算符的构造。我们还提供了两个具体的例子，即各向同性和各向异性海森堡模型。
We present certain classical continuum long wave-length limits of prototype integrable quantum spin chains, and define the corresponding construction of classical continuum Lax operators. We also provide two specific examples, i.e. the isotropic and anisotropic Heisenberg models.
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We present a general method of folding an integrable spin chain, defined on a line, to obtain an integrable open spin chain, defined on a half-line. We illustrate our method through two fundamental models with sl(2) Lie algebra symmetry: the Heisenberg XXX and the Inozemtsev hyperbolic spin chains. We obtain new long-range boundary Hamiltonians and demonstrate that they exhibit Yangian symmetries, thus ensuring integrability of the models we obtain. The method presented provides a "bottom-up" approach for constructing integrable boundaries and can be applied to any spin chain model.
Integrable open elliptic Toda chain with boundaries
本文提出了一种通过Lax矩阵因子化和与XYZ链的规范等价性来构造带有边界项的开放椭圆Toda链的方法。
For integrable inhomogeneous supersymmetric spin chains (generalized graded magnets) constructed employing Y(gl(N|M))-invariant R-matrices in finite-dimensional representations we introduce the master T-operator which is a sort of generating function for the family of commuting quantum transfer matrices. Any eigenvalue of the master T-operator is the tau-function of the classical mKP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0-th time of the hierarchy. This implies a remarkable relation between the quantum supersymmetric spin chains and classical many…
Exact overlaps for "all" integrable matrix product states of rational spin chains
针对有理自旋链中可积矩阵乘积态（MPS）与贝特态的重叠问题，提出通用重叠公式，结果为高汀行列式比值与前因子的乘积，明确了高汀行列式与自旋链的关联性及前因子对𝔤𝔩_N等对称自旋链所有可积MPS的适用性。
Integrable hydrodynamic chains for WZNW model
得到了具有$SU(2)$、$SO(3)$、$SP(2)$和$SU(\infty )$常挠率的WZNW模型的新的可积流体动力学方程
Exact solution of the quantum integrable $D^{(2)}_2$ spin chain with generic integrable boundary fields is constructed. It is found that the transfer matrix of this model can be factorized as the product of those of two open staggered anisotropic XXZ spin chains. Based on this identity, the eigenvalues and Bethe ansatz equations of the $D^{(2)}_2$ model are derived via off-diagonal Bethe ansatz.
Systematic classical continuum limits of integrable spin chains and emerging novel dualities
我们研究了某些经典连续长波极限的原型可积量子自旋链。我们定义了经典连续Lax算子的相应构造。我们的讨论从XXX链、各向异性海森堡模型及其推广开始，并扩展到一般的各向同性和各向异性gl_n磁体。某些经典和量子可积模型出现的特殊“对偶”的量子自旋链，参数化的c-数矩阵，也提出。
We study integrable open boundary conditions for d(2,1;α)^2 and psu(1,1|2)^2 spin-chains. Magnon excitations of these open spin-chains are mapped to massive excitations of type IIB open superstrings ending on D-branes in the AdS_3 x S^3 x S^3 x S^1 and AdS_3 x S^3 x T^4 supergravity geometries with pure R-R flux. We derive reflection matrix solutions of the boundary Yang-Baxter equation which intertwine representations of a variety of boundary coideal subalgebras of the bulk Hopf superalgebra. Many of these integrable boundaries are matched to D1- and D5-brane maximal giant gravitons.
Bethe/Gauge Correspondence for $A_N$ Spin Chains with Integrable Boundaries
本文继续综述 Bethe/规范对应，系统收集具有一般可积边界的各类自旋链的 Bethe ansatz 方程，并与 BCD 型规范群箭图规范理论的真空方程比较，发现并非所有真空方程都能对应已知可积自旋链模型。
We study the integrable crosscap states of the integrable quantum spin chains and we classify them for the $\mathfrak{gl}(N)$ symmetric models. We also give a derivation for the exact overlaps between the integrable crosscap states and the Bethe states. The first part of the derivation is to calculate sum formula for the off-shell overlap. Using this formula we prove that the normalized overlaps of the multi-particle states are ratios of the Gaudin-like determinants. Furthermore we collect the integrable crosscap states which can be relevant in the AdS/CFT correspondence.
Algebraic representation of correlation functions in integrable spin chains
本文以XXZ链为例，综述了最近得到的可积自旋链中关联函数的代数表示。我们改写了以前的公式的形式，同样适用于物理上有趣的齐次链。我们还讨论了量子群不变算子的情形以及推广到XYZ链的情形。
Recursion Relations for Long-Range Integrable Spin Chains with Open Boundary Conditions
众所周知，具有周期性边界条件的短程（例如最近邻）自旋链的可积电荷可以通过所谓的boost算子递归地产生。在过去，这种迭代构造已经被推广到周期性的长程自旋链，因为它们出现在规范/引力对应的上下文中。在这里，我们介绍了递归关系的开放远程自旋链电荷转换成一个长期的短程可积模型。
Boosting Nearest-Neighbour to Long-Range Integrable Spin Chains
我们提出了一个保积递推关系的显式构造的长程自旋链哈密顿量。这些链是Haldane-Shastry和Inozemtsev模型的推广，它们在弦/规范对偶性的最新进展中发挥了重要作用。该方法是基于任意近邻可积自旋链，它揭示了变形参数的模空间。我们还导出了闭链渐近Bethe方程。
Baxterized Solutions of Reflection Equation and Integrable Chain Models
给出了仿射Hecke代数和仿射Birman-Murakami-Wenzl代数的反射方程的非多项式化解，讨论了它们与具有非平凡边界条件的可积自旋链模型的关系.
On the evaluation of form factors and correlation functions for the integrable spin-s XXZ chains via the fusion method
修正了以前文献的推导，对于可积的自旋- $s$ XXZ链，我们用自旋-1/2 XXZ链的标量积上的单个和来表示任何形状因子.用修正的方法，我们用多重积分的单个和来表示零温下任意给定项的自旋- $s$ XXZ关联函数。
We classify all fundamental integrable spin chains with two-dimensional local Hilbert space which have regular R-matrices of difference form. This means that the R-matrix underlying the integrable structures is of the form R(u,v)=R(u-v) and reduces to the permutation operator at some particular point. We find a total of 14 independent solutions, 8 of which correspond to well-known eight or lower vertex models. The remaining 6 models appear to be new and some have peculiar properties such as not being diagonalizable or being nilpotent. Furthermore, for even R-matrices, we find a bijection betwe…
Spectral equivalences and symmetry breaking in integrable SU_q(N) spin chains with boundaries
本文考虑了具有对角和非对角可积边界项的SU_q（N）不变自旋链。通过对具有不同类型边界项的自旋链的代数研究，得到了具有纯对角边界项的可积链与一端具有任意非对角边界项的可积链之间的谱等价关系.对于每一个对角边界项的选择，有一个等谱单边界问题，反之亦然。量子群SU_q（N）的对称性由于非对角边界项的存在而被破坏，然而人们可以利用对角链的谱等价性来容易地理解系统的剩余对称性。
Nested off-diagonal Bethe ansatz and exact solutions of the su(n) spin chain with generic integrable boundaries
提出了一种非对角嵌套Bethe算子方法，用于对角化具有一般可积边界的多分量可积模型。作为一个例子，通过构造嵌套的T-Q关系，基于融合转移矩阵之间的算子乘积恒等式和转移矩阵的渐近性质，得到了具有周期和非对角边界的su（n）不变自旋链模型的精确解.
We propose the full system of Baxter Q-functions (QQ-system) for the integrable spin chains with the symmetry of the $D_r$ Lie algebra. We use this QQ-system to derive new Weyl-type formulas expressing transfer matrices in all symmetric and antisymmetric (fundamental) representations through $r+1$ basic Q-functions. Our functional relations are consistent with the Q-operators proposed recently by one of the authors and verified explicitly on the level of operators at small finite length.
Integrable Deformations of the XXZ Spin Chain
我们考虑XXZ自旋链的周期性和开边界条件的可积变形。特别是，我们对所有的长程变形进行分类，并研究它们对光谱的影响。与XXX的情况相比，我们有z自旋，这引起了两个额外的变形：短程磁扭曲和一个新的长程动量依赖扭曲。
Two branches of integrable open quantum-group invariant $D_{n+1}^{(2)}$ quantum spin chains are known. For one branch (epsilon=0), a complete Bethe ansatz solution has been proposed. However, the other branch (epsilon=1) has so far resisted solution. In an effort to address this problem, we consider here the simplest case n=1. We propose a Bethe ansatz solution, which however is not complete, as it describes only the transfer-matrix eigenvalues with odd degeneracy. We also consider a proposal for the missing eigenvalues.
We introduce a new integrable supersymmetric lattice chain which violates fermion conservation and exhibits fermion-hole symmetry. The model displays exponential degeneracy in every eigenstate including the groundstate. This degeneracy is expressed in the possibility to create any number of zero modes reminiscent of Cooper pairs.
Thermodynamic Bethe ansatz equation for osp(1|2) integrable spin chain
热力学Bethe ansatz应用于与李超代数osp（1）相关的量子可积自旋链|2）。利用弦假设，我们导出了一组无穷多个表征自由能的非线性积分方程（热力学Bethe不等式）。讨论了自由能的低温极限。
Complete Bethe Ansatz solution of the open spin-s XXZ chain with general integrable boundary terms
我们认为开放的自旋-sXXZ量子自旋链与N个网站和一般可积边界项的一般值的体各向异性参数，并为满足一定的约束条件的边界参数的值。我们推导出两组Bethe Answer方程，并找到数值证据，它们一起给出了完整的一套$(2s+1)^{N}$特征值的传输矩阵。对于s=1的情况下，我们明确确定的哈密顿量，并找到一个表达式，其特征值的贝特根。
Chiral Integrable Boundary States of ABJM Spin Chain from Reflection Equations
本文基于反射方程和融合程序，构建ABJM旋链中2n-site chiral可积矩阵积态，并推导四site chiral可积态与Bethe态的精确重叠公式，同时数值研究chiral可积子空间。
We discuss relation between the cluster integrable systems and spin chains in the context of their correspondence with 5d supersymmetric gauge theories. It is shown that $\mathfrak{gl}_N$ XXZ-type spin chain on $M$ sites is isomorphic to a cluster integrable system with $N \times M$ rectangular Newton polygon and $N \times M$ fundamental domain of a 'fence net' bipartite graph. The Casimir functions of the Poisson bracket, labeled by the zig-zag paths on the graph, correspond to the inhomogeneities, on-site Casimirs and twists of the chain, supplemented by total spin. The symmetricity of clust…
Integrable models on Rydberg atom chains
本文系统研究了受限Hilbert空间下的Rydberg原子自旋链可积模型，提出可积性条件并构建了新模型，完成了范围3和4的对称可积Hamilton量分类，发现了与黄金比例相关的临界点。
On integrable Hamiltonians for higher spin XXZ chain
用自旋生成元构造了高自旋周期XXZ链的可积哈密顿量，给出了自旋高达3/2的显式例子。研究了U_q（sl_2）-对称和U（1）-对称泛r-矩阵的Hamilton算子之间的关系，并研究了它们的性质.对高自旋周期链哈密顿量的一种修正，得到了开链的U_q（sl_2）对称可积哈密顿量。
A family of A_{2n}^(2) integrable open spin chains with U_q(C_n) symmetry was recently identified in arXiv:1702.01482. We identify here in a similar way a family of A_{2n-1}^(2) integrable open spin chains with U_q(D_n) symmetry, and two families of D_{n+1}^(2) integrable open spin chains with U_q(B_n) symmetry. We discuss the consequences of these symmetries for the degeneracies and multiplicities of the spectrum. We propose Bethe ansatz solutions for two of these models, whose completeness we check numerically for small values of n and chain length N. We find formulas for the Dynkin labels i…
Spin chain from membrane and the Neumann-Rosochatius integrable system
我们在AdS_4 x S^7中发现了膜构型，它对应于SU（2）可积自旋链的连续极限，被认为是SU（3）自旋链的极限，产生于四维N=4 SYM中，与AdS_5 x S^5中的弦对偶。我们还讨论了与Neumann-Rosochatius可积系统在拉格朗日层次上的关系，比较弦和膜的情况。
Long-Range Deformations for Integrable Spin Chains
我们提出了一个显式构造可积自旋链哈密顿量与长程相互作用的递归关系。基于任意短程（例如最近邻）可积自旋链，它允许构建一组无限的守恒长程电荷。我们用不同类的生成算子来解释变形参数的模空间。长程Bethe方程的快度图和Dressing相就是这些变形的结果。导出了长程自旋链在一般对称代数下变换的闭链渐近Bethe方程。值得注意的是，我们的结构适用于标准最近邻链的推广，如交替自旋链。我们还讨论了它在平面D = 4，N = 4和D = 3，N = 6超对称规范理论中应用的有关性质。最后，我们提出了一个远程和非均匀自旋链之间的映射，提供更多的洞察这些模型的结构以及它们在包装顺序的限制。
Form factors of integrable higher-spin XXZ chains and the affine quantum-group symmetry
我们通过代数Bethe-analgesic方法精确地导出了可积高自旋XXZ链的标积和形状因子。这里的自旋值是任意的，不同的自旋可以混合。我们证明了XXZ自旋链的单值矩阵的仿射量子群对称性$U_q(\hat{sl_2})$，并得到了精确的表达式。此外，通过量子群对称性，我们明确地导出了自旋为1/2的XXZ自旋链的$F$ -基中的$B$和$C$算符的对角化形式，这在XXZ关联函数的代数Bethe-anomaly计算中得到了证明.这些结果对于系统地研究与可积XXZ自旋链相关的各种可解模型的形状因子和关联函数具有重要意义。
Based on the inhomogeneous T-Q relation and the associated Bethe Ansatz equations obtained via the off-diagonal Bethe Ansatz, we construct the Bethe-type eigenstates of the SU(2)-invariant spin-s chain with generic non-diagonal boundaries by employing certain orthogonal basis of the Hilbert space.
We develop a new method to compute the exact overlaps between integrable boundary states and on-shell Bethe states for integrable spin chains. Our method is based on the coordinate Bethe Ansatz and does not rely on the "rotation trick" of the corresponding lattice model. It leads to a rigorous proof of the factorized overlap formulas in a number of cases, some of which were inaccessible to earlier methods. As concrete examples, we consider the compact XXX and XXZ Heisenberg spin chains, and the non-compact $SL(2,\mathbb{R})$ spin chain.
We calculate the scalar product of Bethe states of the XXZ spin-$\frac{1}{2}$ chain with general integrable boundary conditions. The off-shell equations satisfied by the transfer matrix and the off-shell Bethe vectors allow one to derive a linear system for the scalar product of off-shell and on-shell Bethe states. We show that this linear system can be solved in terms of a compact determinant formula that involves the Jacobian of the transfer matrix eigenvalue and certain q-Pochhammer polynomials of the boundary couplings.
Form factors of integrable Heisenberg (higher) spin chains
本文给出了一般可积XXX海森堡自旋链的自旋算符的形状因子的行列式公式。结果适用于任何“混合”自旋链，如交替自旋链，或自旋链与磁性杂质。
Long-Range GL(n) Integrable Spin Chains and Plane-Wave Matrix Theory
量子自旋链自然产生于微扰大N场论和矩阵模型。这种模型的哈密顿量是最近邻型相互作用的长程变形。在这里，我们研究了最一般的长程可积自旋链，自旋在gl（n）的基本表示中变换。我们导出了在前四个微扰阶下的哈密顿量和相应的渐近Bethe不等式。此外，我们提出了所有阶的Bethe方程，并确定了可积系统的模。最后，我们将我们的结果应用到平面波矩阵理论，并表明，在一个封闭的部门的哈密顿量是不是这种形式，因此不可积超过第一微扰阶。这也意味着完整的模型是不可积的。
Quantum Group U_q(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain
我们展示了可积的高自旋XXX和XXZ自旋链的关联函数之间的对称关系，其中我们明确地评估了自旋为1的情况下代表一点函数的多重积分。我们回顾了可积高自旋XXZ链的关联函数的多重积分表示，该链是在包括反铁磁点在内的无质量区域中导出的。在这里，我们利用对称和非对称R-矩阵之间的规范变换，分别对应于主分次和齐次分次，我们将非齐次参数发送到完整的2s-弦集合。在自旋为1的情况下，我们也给出了一点函数的解析表达式的数值支持。
With the XXZ spin chains as examples, we prove two theorems: (1) the functional relations derived from the off-diagonal Bethe Ansatz scheme are the sufficient and necessary conditions to characterize the complete spectrum of the corresponding transfer matrix; (2) each eigenvalue of the transfer matrix can be parameterized by a minimal inhomogeneous T-Q relation. These statements hold for both with and without inhomogeneity. The proof can be generalized to other finite-dimensional quantum integrable models.
Integral equations for thermodynamics of the osp(1|2s) integrable spin chain
我们提出了一个非线性积分方程组（NLIE），它给出了osp（1）的自由能|2s）可积自旋链。与通常的热力学Bethe方程相比，我们的新NLIE只包含有限个未知函数。在推导NLIE时，我们使用我们的osp（1| 2s）版本的T-系统和量子转移矩阵方法。在此基础上，我们还计算了自由能和比热的高温膨胀。
Separation of Variables in the Classical Integrable SL(3) Magnetic Chain
哈密顿可积系统理论研究两个基本问题：运动方程的积分和作用角变量的构造。然而，第三个问题应列入清单：变量分离。虽然它比其它两个方程简单得多，但它与量子可积性有着重要的关系。对非超椭圆代数曲线可积模型的一个例子--$SL(3)$磁链构造了分离变量法。
Symmetry, Integrable Chain Models and Stochastic Processes
给出了构造具有一定李代数对称性或量子李代数对称性的链模型的一般方法。这些对称模型产生一系列的可积系统。作为例子，讨论了具有$A_n$对称性的链模型及其相关的Temperley-Lieb代数结构和表示.结果表明，对应于这些$A_n$对称可积链模型，存在精确可解的平稳离散时间模型（分别为连续时间）马尔可夫链，其转移矩阵的谱（分别为强度矩阵）与相应的可积模型的强度矩阵相同。
Algebraic aspects of the correlation functions of the integrable higher-spin XXZ spin chains with arbitrary entries
本文讨论了XXZ自旋链的一些基本性质，这些性质在自旋S XXZ关联函数的多重积分表示与初等矩阵的任意乘积的代数Bethe-anomaly推导中是重要的.例如，我们构造了无质量体系中的厄米共轭矢量，并引入了自旋-s厄米基本矩阵。
We present new integrable models of interacting spin-1/2 chains, which can be interpreted as hard rod deformations of the XXZ Heisenberg chains. The models support multiple particle types: dynamical hard rods of length $\ell$ and particles with lengths $\ell'<\ell$ that are immobile except for the interaction with the hard rods. We encounter a remarkable phenomenon in these interacting models: exact spectral degeneracies across different deformations and volumes. The algebraic integrability of these systems is also treated using a recently developed formalism for medium range integrable spin c…
Building on arXiv:1804.01998 we investigate the integrable structure of the Wess-Zumino-Witten (WZW) model describing closed strings on $AdS_3\times S^3\times T^4$. Using the recently-proposed integrable S matrix we show analytically that all wrapping corrections cancel and that the theory has a natural spin-chain interpretation. We construct the integrable spin chain and discuss its relation with the WZW description. Finally we compute the spin-chain spectrum in closed form and show that it matches the WZW prediction on the nose.
High-energy scattering in gauge theories and integrable spin chains
在主导对数近似和广义$N_C$中，两个费米子和一个胶子区域子的相互作用由对应于开自旋链的可积系统描述。
The graded off-diagonal Bethe ansatz method is proposed to study supersymmetric quantum integrable models (i.e., quantum integrable models associated with superalgebras). As an example, the exact solutions of the $SU(2|2)$ vertex model with both periodic and generic open boundary conditions are constructed. By generalizing the fusion techniques to the supersymmetric case, a closed set of operator product identities about the transfer matrices are derived, which allows us to give the eigenvalues in terms of homogeneous or inhomogeneous $T-Q$ relations. The method and results provided in this pa…
Finding out root patterns of quantum integrable models is an important step to study their physical properties in the thermodynamic limit. Especially for models without $U(1)$ symmetry, their spectra are usually given by inhomogeneous $T-Q$ relations and the Bethe root patterns are still unclear. In this paper with the antiperiodic $XXZ$ spin chain as an example, an analytic method to derive both the Bethe root patterns and the transfer-matrix root patterns in the thermodynamic limit is proposed. Based on them the ground state energy and elementary excitations in the gapped regime are derived.…
Generalized Integrable Boundary States in XXZ and XYZ Spin Chains
研究周期或扭曲边界条件下各向异性海森堡链的可积边界态，通过KT-关系构造因子化可积边界态，并给出Bethe根的显式选择规则。
Yang-Mills Correlation Functions from Integrable Spin Chains
N=4的杨-米尔斯理论的伸缩算符与可积自旋链之间的关系使得计算该理论中所有算符的单圈反常维数成为可能。本文介绍了如何将可积自旋链技术应用于杨-米尔斯关联函数的计算，将其表示为相应自旋链上自旋算符的矩阵元。我们用XXX_1/2链描述的SU（2）扇区中的几个例子来说明这种方法。
The continuum limit of the integrable open XYZ spin-1/2 chain
利用微扰方法证明了半直线上可积XYZ自旋1/2链的连续极限可导出边界sine-Gordon理论。
Two-dimensional Ultra-Toda integrable mappings and chains (Abelian case)
引入了一类新的可积映射和可积链。相应的（1+2）可积系统对于这样的离散变换是不变性的，并给出了显式表示.对于给定的群元，它们的类孤子解可用半单A_n代数基本表示的矩阵元表示。
Integrable open spin chains from giant gravitons
我们证明了在N=4 SYM中存在极大巨引力子态时，与巨引力子相连的开弦对偶态产生PSU（2，2|（4）自旋链的SO（6）扇区内具有可积边界条件的开自旋链模型。
Integrable XYZ Spin Chain with Boundaries
本文考虑一类与可积性相容的开XYZ自旋1/2链的边界项。利用八顶点模型的$R$-矩阵得到了满足边界Yang-Baxter方程的$K$-矩阵的一般椭圆解，并导出了相应的可积自旋链哈密顿量.
In arXiv:1704.05807, it was shown that the planar flavored ABJM theory is integrable in the scalar sector at two-loop order using coordinate Bethe ansatz. A salient feature of this case is that the boundary reflection matrices are anti-diagonal with respect to the chosen basis. In this paper, we relax the coefficients of the boundary terms to be general constants in order to search for integrable systems among this class. We found that at each end of the spin chain, the only integrable boundary interaction, besides the one in arXiv:1704.05807, is the one with vanishing boundary interactions le…
Generalized Hydrodynamics is a recent theory that describes the large scale transport properties of one dimensional integrable models. At the heart of this theory lies an exact quantum-classical correspondence, which states that the flows of the conserved quantities are essentially quasi-classical even in the interacting quantum many body models. We provide the algebraic background to this observation, by embedding the current operators of the integrable spin chains into the canonical framework of Yang-Baxter integrability. Our construction can be applied in a large variety of models including…
Integrable $1/r^2$ Spin Chain with Reflecting End
引入了一种新的Haldane-Shastry型可积自旋链。它被解释为具有{ \it反射端}的平方反比相互作用自旋链。该模型的格点由拉盖尔多项式零点的平方根组成。使用“交换算子形式”，明确地构造了模型的运动积分。
Open Perturbatively Long-Range Integrable gl(N) Spin Chains
我们构造了自旋在gl（N）基本表示和开边界条件下变换的最一般的长程微扰可积自旋链。除了先前确定的体积模量，我们发现一组新的参数确定的反射相移。我们还考虑有限大小的贡献和评论他们的决心。
Multi-parameter deformed and nonstandard $Y(gl_M)$ Yangian symmetry in integrable variants of Haldane-Shastry spin chain
利用置换代数的“类任意子”表示，在交换两个格点的自旋时提取非平凡的相位因子，我们构造了Haldane-Shastry（HS）自旋链的一些可积变体.这些自旋链的Lax方程允许我们找出相关的守恒量。然而，事实证明，这样的自旋链也拥有一些额外的守恒量，这些守恒量显然不能从拉克斯方程推导出来。识别这些额外的保守量，和通常的相关的Lax方程，与不同模式的monodromy矩阵，它表明，上述HS一样的自旋链表现出多参数变形和“非标准”的变体的$Y(gl_M)$ Yangian对称性。
Chiral Integrable Boundary States in the SU(4) Alternating Spin Chain
本文在SU(4)交替自旋链中提出手性可积边界态，利用两环拉廷算符和非扭曲可积条件，识别出特定基态并计算其与本征态的重叠。
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