Boundary conditions for integrable quantum systems

DOI10.1088/0305-4470/21/10/015zbMath0685.58058OpenAlexW2122047152WikidataQ59722045 ScholiaQ59722045MaRDI QIDQ4735840

Evgueni K. Sklyanin

Publication date: 1988

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/9f79bd3ca6d5e59d179b2509e1efc5dc2f97182a

zbMATH Keywords

nonlinear Schrödinger equationToda chainR-matrixopen quantum chains

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Exactly solvable models; Bethe ansatz (82B23) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Groups and algebras in quantum theory and relations with integrable systems (81R12) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

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Abstracts from the mini-workshop held March 20--26, 2022 ⋮ Mini-workshop: Three facets of \(R\)-matrices. Abstracts from the mini-workshop held October 17--23, 2021 (hybrid meeting) ⋮ Baxterization of solutions to reflection equation with Hecke \(R\)-matrix. ⋮ On the \(h\)-adic quantum vertex algebras associated with Hecke symmetries ⋮ Spectrum of the transfer matrices of the spin chains associated with the \(A^{(2)}_3\) Lie algebra ⋮ The half-infinite XXZ chain in Onsager's approach ⋮ Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions ⋮ Off-diagonal Bethe ansatz solutions of the anisotropic spin-\(\frac{1}{2}\) chains with arbitrary boundary fields ⋮ Exact solution of the one-dimensional Hubbard model with arbitrary boundary magnetic fields ⋮ Correlation functions of the half-infinite XXZ spin chain with a triangular boundary ⋮ Bethe subalgebras in Hecke algebra and Gaudin models ⋮ Centers of generalized reflection equation algebras ⋮ Wronskian-type formula for inhomogeneous \(TQ\) equations ⋮ NLIE and finite size effects of the spin-1/2 XXZ and sine-Gordon models with two boundaries revisited ⋮ A dual construction of the isotropic Landau-Lifshitz model ⋮ Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains ⋮ Quantum-classical duality for Gaudin magnets with boundary ⋮ Set-theoretic Yang-Baxter \& reflection equations and quantum group symmetries ⋮ Murphy elements from the double-row transfer matrix ⋮ Universal Baxter TQ-relations for open boundary quantum integrable systems ⋮ Exact solutions of the \(C_n\) quantum spin chain ⋮ A conjecture concerning the \(q\)-Onsager algebra ⋮ Darboux-Nijenhuis variables for open generalized Toda chains ⋮ Multiple reference states and complete spectrum of the \(\mathbb Z_{n}\) Belavin model with open boundaries ⋮ The generalized non-linear Schrödinger model on the interval ⋮ Functional relations from the Yang-Baxter algebra: Eigenvalues of the \(XXZ\) model with non-diagonal twisted and open boundary conditions ⋮ The alternating presentation of \(U_q(\widehat{gl_2})\) from Freidel-Maillet algebras ⋮ Integrable spin-boson models descending from rational six-vertex models ⋮ New integrable Gaudin-type systems, classical \(r\)-matrices and quasigraded Lie algebras ⋮ Solution of the \(\text{SU}(N)\) vertex model with non-diagonal open boundaries ⋮ Diagonal solutions to reflection equations in higher spin models ⋮ The Uq(sln∧) analogue of the XXZ chain with a boundary ⋮ Quantum Toda chains intertwined ⋮ Completeness of SoV representation for \(\mathrm{SL}(2,\mathbb{R})\) spin chains ⋮ Solution of the dual reflection equation for An−1(1) solid-on-solid model ⋮ Solving the quantum nonlinear Schrödinger equation with δ-type impurity ⋮ Spin current in quantum \(XXZ\) spin chain ⋮ Revisiting the \(Y=0\) open spin chain at one loop ⋮ Nonstandard comodules for quantum matrix bialgebras ⋮ Coordinate Bethe ansatz for the one-dimensional SU(n) Hubbard model with open boundary conditions ⋮ Integrable extended Hubbard models with boundary Kondo impurities ⋮ The Kowalewski top: A new Lax representation ⋮ Jordanian deformation of the open XXX spin chain ⋮ Integrable quadratic Hamiltonians with a linear Lie-Poisson bracket ⋮ Exact solution of the \(A_2^{(2)}\) model with non-diagonal boundary reflections ⋮ Why scalar products in the algebraic Bethe ansatz have determinant representation ⋮ Boundary scattering in the \({\varphi}^6\) model ⋮ Combinatorial solutions to the reflection equation ⋮ Wave functions for quantum integrable particle systems via partial confluences of multivariate hypergeometric functions ⋮ Boundary matrices for the higher spin six vertex model ⋮ Off-diagonal Bethe Ansatz on the \textit{so}(5) spin chain ⋮ New integrable boundary conditions for the Ablowitz-Ladik model: from Hamiltonian formalism to nonlinear mirror image method ⋮ On complex gamma-function integrals ⋮ Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions ⋮ Noncommutative extensions of elliptic integrable Euler–Arnold tops and Painlevé VI equation ⋮ Exact solution of the $ sp(4) $ integrable spin chain with generic boundaries ⋮ Gauge theory and boundary integrability ⋮ A topological origin of quantum symmetric pairs ⋮ Lax pair and boundary \(K\)-matrices for the one-dimensional Hubbard model ⋮ DAHA and skein algebra of surfaces: double-torus knots ⋮ Matrix product solution to the reflection equation associated with a coideal subalgebra of \(U_q(A^{(1)}_{n-1})\) ⋮ Scalar products in twisted XXX spin chain. Determinant representation ⋮ Vertex models and spin chains in formulas and pictures ⋮ New $D_{n+1}^{(2)}$ K-matrices with quantum group symmetry ⋮ Bogomolny-Prasad-Sommerfeld monopoles and open spin chains ⋮ On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models ⋮ A bispectral q-hypergeometric basis for a class of quantum integrable models ⋮ Koornwinder polynomials and the \(XXZ\) spin chain ⋮ TRIGONOMETRIC sℓ(2) GAUDIN MODEL WITH BOUNDARY TERMS ⋮ Connection problems for quantum affine KZ equations and integrable lattice models ⋮ Antiperiodic XXZ chains with arbitrary spins: complete eigenstate construction by functional equations in separation of variables ⋮ Nonstandard representations of type \(C\) affine Hecke algebra from \(K\)-operators. ⋮ Boundary Effects on the Supersymmetric Sine-Gordon Model Through Light-Cone Lattice Regularization ⋮ Pseudo-symmetric pairs for Kac-Moody algebras ⋮ Hidden local gauge invariance in the one-dimensional Heisenberg XXZ model with the general boundary terms ⋮ Preparing exact eigenstates of the open XXZ chain on a quantum computer ⋮ EXACT RESULTS FOR THE ONE-DIMENSIONAL MANY-BODY PROBLEM WITH CONTACT INTERACTION: INCLUDING A TUNABLE IMPURITY ⋮ Introduction to classical and quantum integrability ⋮ On diagonal solutions of the reflection equation ⋮ Exact solution of the B ₁ model ⋮ Time and band limiting operator and Bethe ansatz ⋮ Surface energy and elementary excitations of the XXZ spin chain with arbitrary boundary fields ⋮ Extended T-systems, Q matrices and T-Q relations for $ \newcommand{\e}{{\rm e}} s\ell(2)$ models at roots of unity ⋮ Truncation of the reflection algebra and the Hahn algebra ⋮ Reflection $\boldsymbol{K}$ matrices associated with an Onsager coideal of $\boldsymbol{U_p(A^{(1)}_{n-1})}, \boldsymbol{U_p(B^{(1)}_{n})}, $ $ \boldsymbol{U_p(D^{(1)}_{n})}$ and $\boldsymbol{U_p(D^{(2)}_{n+1})}$ ⋮ Generic triangular solutions of the reflection equation: ${U}_{q}\left(\hat{s{l}_{2}}\right)$ case ⋮ A Q-operator for open spin chains I. Baxter’s TQ relation ⋮ Discretizations of the generalized AKNS scheme ⋮ Boundary emptiness formation probabilities in the six-vertex model at $\mathbf{\Delta }=-\frac{\mathbf{1}}{\mathbf{2}}$ ⋮ One-point functions in AdS/dCFT ⋮ Exact solution of an integrable anisotropic $\boldsymbol{J_1-J_2}$ spin chain model ⋮ On the classification of rational K-matrices ⋮ Superintegrability of Generalized Toda Models on Symmetric Spaces ⋮ COIDEAL SUBALGEBRAS IN QUANTUM AFFINE ALGEBRAS ⋮ Difference Calogero–Moser systems and finite Toda chains ⋮ The Klein-Gordon Equation on the Half Line: a Riemann-Hilbert Approach ⋮ Spin chains and Gustafson’s integrals ⋮ Boundary perimeter Bethe ansatz ⋮ Universal K-matrices for quantum Kac-Moody algebras ⋮ Continuous representations of scalar products of Bethe vectors ⋮ Correlation functions of the XXZ spin chain with the twisted boundary condition ⋮ Reflection matrices withU_q[osp⁽²⁾(2|2m) symmetry] ⋮ Algebraic framework for quantization of nonultralocal models ⋮ Lax formalism for a family of integrable Toda-related n-particle systems ⋮ On separation of variables for reflection algebras ⋮ Boundary correlations for the six-vertex model with reflecting end boundary condition ⋮ Eigenstates of triangularisable open XXX spin chains and closed-form solutions for the steady state of the open SSEP ⋮ On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions ⋮ Delta-Bose gas on a half-line and the Kardar–Parisi–Zhang equation: boundary bound states and unbinding transitions ⋮ The Am(1) Q-system ⋮ Separation of variables for quadratic algebras: Algebras of Maillet and reflection-equation algebras ⋮ Truncation identities for the small polaron fusion hierarchy ⋮ Diagonalization of transfer matrix of supersymmetry $U_{q}(\widehat{sl}(M+1|N+1))$Uq(sl̂(M+1|N+1)) chain with a boundary ⋮ Arctic curve of the free-fermion six-vertex model with reflecting end boundary condition ⋮ Twisted Yangians, twisted quantum loop algebras and affine Hecke algebras of type $BC$ ⋮ Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables ⋮ PERMUTATION GROUP APPROACH TO THE ONE-DIMENSIONAL XXX HEISENBERG OPEN SPIN-1/2 CHAINS ⋮ Time-dependent defects in integrable soliton equations ⋮ THE LUTTINGER LIQUID AND INTEGRABLE MODELS ⋮ EXACT SOLVING q DEFORMED BOSON MODEL UNDER OPEN BOUNDARY CONDITION ⋮ On boundary fusion and functional relations in the Baxterized affine Hecke algebra ⋮ Heun operator of Lie type and the modified algebraic Bethe ansatz ⋮ A note on a boundary sine-Gordon model at the free-Fermion point ⋮ A tale of two Bethe ansätze ⋮ Overlaps with arbitrary two-site states in the XXZ spin chain ⋮ A deformed analogue of Onsager’s symmetry in the XXZ open spin chain ⋮ Boundary qKZ equation and generalized Razumov–Stroganov sum rules for open IRF models ⋮ Boundary non-local charges from the open spin chain ⋮ Analytical Bethe ansatz for closed and opengl(Script N)-spin chains in any representation ⋮ Spin chains from dynamical quadratic algebras ⋮ Bethe ansatz derived from the functional relations of the openXXZchain for new special cases ⋮ GeneralizedT–Qrelations and the open XXZ chain ⋮ The Temperley–Lieb algebra and its generalizations in the Potts andXXZmodels ⋮ Logarithmic minimal models ⋮ osp(1|2) off-shell Bethe ansatz equation with boundary terms ⋮ INTRODUCTION TO YANGIAN SYMMETRY IN INTEGRABLE FIELD THEORY ⋮ FROM DEFECTS TO BOUNDARIES ⋮ ANALYTICAL BETHE ANSATZ FOR OPEN SPIN CHAINS WITH SOLITON NONPRESERVING BOUNDARY CONDITIONS ⋮ Physical combinatorics and quasiparticles ⋮ A boundary matrix for AdS/CFTSU(1|1) spin chain ⋮ Quantum group symmetries and completeness for $\boldsymbol {A}_{\boldsymbol {2n}}^{\boldsymbol{(2)}}$ open spin chains ⋮ GAUDIN MAGNET WITH IMPURITY AND ITS GENERALIZED KNIZHNIK–ZAMOLODCHIKOV EQUATION ⋮ Higher rank classical analogs of the Askey-Wilson algebra from the sl_N Onsager algebra ⋮ The openXXZand associated models atqroot of unity ⋮ On , , , , , , and reflectionK-matrices ⋮ Loop model with mixed boundary conditions,qKZ equation and alternating sign matrices ⋮ The algebraic Bethe ansatz for open vertex models ⋮ Correlation functions of the openXXZchain: I ⋮ Quantum Knizhnik–Zamolodchikov equation: reflecting boundary conditions and combinatorics ⋮ The thermodynamical limit of generalgl(N) spin chains: the vacuum state and densities ⋮ Exact spectrum of the XXZ open spin chain from theq-Onsager algebra representation theory ⋮ A complete Bethe ansatz solution for the open spin-s XXZchain with general integrable boundary terms ⋮ On the emptiness formation probability of the openXXZspin-1/2 chain ⋮ Boundary transfer matrices and boundary quantum KZ equations ⋮ On the elliptic sinh–Gordon equation with integrable boundary conditions ^* ⋮ On osp(M?2n) Integrable Open Spin Chains ⋮ On boundary superalgebras ⋮ Symmetries of spin systems and Birman–Wenzl–Murakami algebra ⋮ Hydrodynamic type integrable equations on a segment and a half-line ⋮ ON A SYSTEMATIC APPROACH TO DEFECTS IN CLASSICAL INTEGRABLE FIELD THEORIES ⋮ Correlation functions of the openXXZchain: II ⋮ T-Q relations for the integrable two-species asymmetric simple exclusion process with open boundaries ⋮ Yang–Baxter integrable dimers on a strip ⋮ The open XXZ chain at Δ = −1/2 and the boundary quantum Knizhnik–Zamolodchikov equations ⋮ Diagonalization of infinite transfer matrix of boundary Uq,p(AN−1(1)) face model ⋮ Vertex Operator Approach to Semi-infiniteSpin Chain: Recent Progress ⋮ Q-systems with boundary parameters ⋮ Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary ⋮ Towards the solution of an integrable $D_{2}^{(2)}$ spin chain ⋮ The Yang–Baxter paradox ⋮ An algebraic approach to discrete time integrability ⋮ The open XXX spin chain in the SoV framework: scalar product of separate states ⋮ Separation of variables for a flux tube with an end ⋮ Graded off-diagonal Bethe ansatz solution of the \(\operatorname{SU}(2|2)\) spin chain model with generic integrable boundaries ⋮ Algebraic symmetry and self-duality of an open ASEP ⋮ The quantum deformed mirror TBA II ⋮ Integrable boundaries in AdS/CFT: revisiting the \(Z=0\) giant graviton and D7-brane ⋮ \(\mathcal{N}=1 \) super sinh-Gordon model in the half line: breather solutions ⋮ Exact solution of the trigonometric \(\operatorname{SU}(3)\) spin chain with generic off-diagonal boundary reflections ⋮ Algebraic Bethe ansatz for the Temperley-Lieb spin-1 chain ⋮ Universal Bethe ansatz solution for the Temperley-Lieb spin chain ⋮ Periodic integrable systems with delta-potentials ⋮ Twisted Yangians for symmetric pairs of types B, C, D ⋮ Bethe states of the XXZ spin-\(\frac{1}{2}\) chain with arbitrary boundary fields ⋮ Jumps and twists in affine Toda field theories ⋮ Algebraic Bethe ansatz for the \(s\ell(2)\) Gaudin model with boundary ⋮ Off-shell scalar products for the \(XXZ\) spin chain with open boundaries ⋮ Algebraic Bethe ansatz for open XXX model with triangular boundary matrices ⋮ Open Hecke chains and free fermions ⋮ Bethe ansatz and boundary energy of the open \(\mathrm{spin}\)-\(\frac12\) \(XXZ\) chain ⋮ The algebraic Bethe ansatz for the \(\text{Osp}(2|2)\) model with open boundary conditions ⋮ Bethe ansatz equations and exact s matrices for the \(\text{Osp}(M|2n)\) open super-spin chain ⋮ Nested Bethe ansatz for the \(B_N\) vertex model with open boundary conditions ⋮ Exact solution of the \(XXZ\) Gaudin model with generic open boundaries ⋮ \(R\)-matrices and spectrum of vertex models based on superalgebras ⋮ Algebraic Bethe ansatz for the Zamolodchikov-Fateev and Izergin-Korepin models with open boundary conditions ⋮ An integrable structure related with tridiagonal algebras ⋮ Deformed Dolan-Grady relations in quantum integrable models ⋮ A matrix model for branes on WZW simple current orbifolds ⋮ Bethe ansatz for the \(XXX\)-\(S\) chain with non-diagonal open boundaries ⋮ NLIE for hole excited states in the sine-Gordon model with two boundaries ⋮ Spin models and superconformal Yang--Mills theory ⋮ Reflection \(K\)-matrices related to Temperley-Lieb \(R\)-matrices ⋮ Boundary Lax pairs for the \(A_n^{(1)}\) Toda field theories ⋮ Conformal boundary conditions in the critical \({\mathcal O}(n)\) model and dilute loop models ⋮ A note on the boundary spin \(s\) XXZ chain ⋮ Twisting the mirror TBA ⋮ Twisted Bethe equations from a twisted S-matrix ⋮ On the NLIE of (inhomogeneous) open spin-1 XXZ chain with general integrable boundary terms ⋮ Drinfeld twists of the open XXZ chain with non-diagonal boundary terms ⋮ Nested algebraic Bethe ansatz for open \(GL(N)\) spin chains with projected K-matrices ⋮ The spectrum of an open vertex model based on the \(U_q[SU(2)\) algebra at roots of unity] ⋮ Reflection matrices for the \(U_q[sl(r|2m)^{(2)}\) vertex model] ⋮ Exact spin quantum Hall current between boundaries of a lattice strip ⋮ Separation of variables for integrable spin-boson models ⋮ Systematic classical continuum limits of integrable spin chains and emerging novel dualities ⋮ Ground-state phase diagram for a system of interacting, \(D(D_{3})\) non-Abelian anyons ⋮ Determinant formula for the partition function of the six-vertex model with a non-diagonal reflecting end ⋮ Domain wall partition function of the eight-vertex model with a non-diagonal reflecting end ⋮ Review of AdS/CFT integrability, chapter IV.2: Deformations, orbifolds and open boundaries ⋮ Coideal algebras from twisted Manin triples ⋮ Open spin chain and open spinning string ⋮ Generalized coordinate Bethe ansatz for non-diagonal boundaries ⋮ The spectral problem for strings on twisted \(\text{AdS}_{5}\times \text{S}^{5}\) ⋮ Determinant representations for scalar products of the XXZ Gaudin model with general boundary terms ⋮ Excited states NLIE for sine-Gordon model in a strip with Dirichlet boundary conditions ⋮ \(Q\)-operator and \(T\)-\(Q\) relation from the fusion hierarchy ⋮ Modifications of bundles, elliptic integrable systems, and related problems ⋮ Reflection matrices from Hadamard-type Temperley-Lieb \(R\)-matrices ⋮ Jordanian deformation of the open \(s\ell(2)\) Gaudin model ⋮ On maximally superintegrable systems ⋮ The Poisson bracket compatible with the classical reflection equation algebra ⋮ Reduction and realization in Toda and Volterra ⋮ Change of the time for the periodic Toda lattices and natural systems on the plane with higher order integrals of motion ⋮ On an integrable case of Kozlov-Treshchev Birkhoff integrable potentials ⋮ Achiral boundaries and the twisted Yangian of the D5-brane ⋮ Integrability of Green-Schwarz sigma models with boundaries ⋮ Indecomposability parameters in chiral logarithmic conformal field theory ⋮ Generalized Landau-Lifshitz models on the interval ⋮ A note on the IR limit of the NLIEs of boundary supersymmetric sine-Gordon model ⋮ Refined Cauchy/Littlewood identities and six-vertex model partition functions. II: Proofs and new conjectures ⋮ Thermodynamic limit and boundary energy of the \(\operatorname{su}(3)\) spin chain with non-diagonal boundary fields ⋮ Spin excitations in the integrable open quantum group invariant supersymmetric \(t\)-\(J\) model ⋮ Orthogonality of Bethe ansatz eigenfunctions for the Laplacian on a hyperoctahedral Weyl alcove ⋮ Drinfeld J presentation of twisted Yangians ⋮ Infinite series of Lie algebras and boundary conditions for integrable systems ⋮ On the \(\mathcal{{U}}_{q}[osp(1|2)\) Temperley-Lieb model] ⋮ On integrable quantum group invariant antiferromagnets ⋮ Exact solution of the alternating XXZ spin chain with generic non-diagonal boundaries ⋮ Finite-size left-passage probability in percolation ⋮ Asymmetric simple exclusion process with open boundaries and Koornwinder polynomials ⋮ Boundary finite size corrections for multiparticle states and planar AdS/CFT ⋮ Determinant representations of scalar products for the open XXZ chain with non-diagonal boundary terms ⋮ Scalar products of the open XYZ chain with non-diagonal boundary terms ⋮ Scattering in the presence of a reflecting and transmitting impurity ⋮ Generalized \(q\)-Onsager algebras and boundary affine Toda field theories ⋮ Generic boundary scattering in the open XXZ chain ⋮ Elliptic dynamical reflection algebra and partition function of SOS model with reflecting end ⋮ The functional method for the domain-wall partition function ⋮ The topological basis realization for six qubits and the corresponding Heisenberg spin-\(\frac {1}{2}\) chain model ⋮ Integrable Wilson loops ⋮ Reunion probabilities of \(N\) one-dimensional random walkers with mixed boundary conditions ⋮ On a family of integrals that extend the Askey-Wilson integral ⋮ Thermodynamic limit and surface energy of the \(XXZ\) spin chain with arbitrary boundary fields ⋮ Classical impurities associated to high rank algebras ⋮ Boundary effects on the supersymmetric sine-Gordon model through light-cone lattice approach ⋮ Gauge theory and boundary integrability. II: Elliptic and trigonometric cases ⋮ Cylinder partition function of the 6-vertex model from algebraic geometry ⋮ Izergin-Korepin analysis on the wavefunctions of the \(U_q(\mathrm{sl}_2)\) six-vertex model with reflecting end ⋮ Many-particle models with two constants of interaction ⋮ Q-operators for the open Heisenberg spin chain ⋮ Integral formula for elliptic SOS models with domain walls and a reflecting end ⋮ Exact solution of an integrable non-equilibrium particle system ⋮ Integrable heat conduction model ⋮ \(U_q[osp(3|2)\) quantum chains with quantum group invariant boundaries] ⋮ Vector NLS solitons interacting with a boundary* ⋮ Exact solution of an anisotropic J ₁–J ₂ model with the Dzyloshinsky–Moriya interactions at boundaries ⋮ Nonlinear mirror image method for nonlinear Schrödinger equation: Absorption/emission of one soliton by a boundary ⋮ Integrable models from singly generated planar algebras ⋮ Boundary symmetry breaking in CFT and the string order parameter ⋮ Bethe/gauge correspondence for ABCDEFG-type 3d gauge theories ⋮ Quadratic algebras and integrable systems ⋮ The \(D_3^{(2)}\) spin chain and its finite-size spectrum ⋮ Generalized Schur-Weyl dualities for quantum affine symmetric pairs and orientifold KLR algebras ⋮ The steady state of the boundary-driven multiparticle asymmetric diffusion model ⋮ A note on constructing quasi modules for quantum vertex algebras from twisted Yangians ⋮ Lax pair formulation for the open boundary Osp(1∣2) spin chain ⋮ Algebraic Bethe ansatz for the open XXZ spin chain with non-diagonal boundary terms via \(U_{\mathfrak{q}}\mathfrak{sl}_2\) symmetry ⋮ Flag integrable models and generalized graded algebras ⋮ Exact solution of a non-Hermitian PT -symmetric spin chain ⋮ Solutions to graded reflection equation of \(\mathrm{GL}\)-type ⋮ Multi-point correlation functions in the boundary XXZ chain at finite temperature ⋮ Kirillov-Reshetikhin modules and quantum \(K\)-matrices ⋮ Spectral analysis of an open \(q\)-difference Toda chain with two-sided boundary interactions on the finite integer lattice ⋮ Unnamed Item ⋮ Supersymmetric, integrable boundary field theories ⋮ Integrable boundary impurities in the \(t\)-\(J\) model with different gradings ⋮ Exact solution of the supersymmetric sinh-Gordon model with boundary. ⋮ Nested Bethe ansatz for Perk-Schultz model with open boundary conditions ⋮ Integrable chain model with additional staggered model parameter ⋮ Soliton \(S\) matrices for the critical \(A^{(1)}_{\mathcal N-1}\) chain. ⋮ Minimal models of integrable lattice theory and truncated functional equations ⋮ Boundary conditions in rational conformal field theories. ⋮ Heisenberg spin chains based on \(\text{sl}(2|1)\) symmetry ⋮ Integrability of the \(D^2_n\) vertex models with open boundary ⋮ The boundary supersymmetric sine-Gordon model revisited ⋮ Asymptotic behavior of singular solitons and the inverse scattering method for solving boundary value problems ⋮ On the classification problem for Birkhoff integrable systems with potentials of exponential type ⋮ D\(_{n+1}^{(2)}\) reflection K-matrices ⋮ Integrable open boundary conditions for the Bariev model of three coupled XY spin chains ⋮ Boundary states and finite size effects in sine-Gordon model with Neumann boundary condition ⋮ A supersymmetric \(U_q[\text{osp}(2|2)\)-extended Hubbard model with boundary fields] ⋮ Finite size effects in boundary sine-Gordon theory ⋮ Solving the open \(XXZ\) spin chain with nondiagonal boundary terms at roots of unity ⋮ The scalar products and the norm of Bethe eigenstates for the boundary \(XXX\) Heisenberg spin-1/2 finite chain ⋮ Bethe ansatz solution for quantum spin-1 chains with boundary terms ⋮ Boundary quantum Knizhnik-Zamolodchikov equations and fusion ⋮ Modified algebraic Bethe ansatz for XXZ chain on the segment. III. Proof ⋮ Boundary algebras and Kac modules for logarithmic minimal models ⋮ The Askey–Wilson algebra and its avatars ⋮ Integrable boundaries for the q-Hahn process ⋮ Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields ⋮ Exact solution of a quantum spin chain with competing bulk and boundary terms ⋮ Scalar product for the XXZ spin chain with general integrable boundaries ^* ⋮ Shor–Movassagh chain leads to unusual integrable model ⋮ Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin ⋮ Integrable boundary conditions for staggered vertex models

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