Boundary conditions for integrable quantum systems

1988/05/21 by E K Sklyanin, E. K. Sklyanin · 38 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · doi:10.1088/0305-4470/21/10/015

openalex publication_date 1988/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

A new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering (R-matrix) method. The method proposed allows the author to treat open quantum chains with appropriate boundary terms in the Hamiltonian. The general considerations are applied to the XXZ and XYZ models, the nonlinear Schrodinger equation and Toda chain.

Cited by

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• Universal TT- and TQ-relations via centrally extended q-Onsager algebra
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• Minimalistic Presentation and Coideal Structure of Twisted Yangians
• Exact strong zero modes in quantum circuits and spin chains with non-diagonal boundary conditions
• XYZ integrability the easy way
• Non-invertible Kramers-Wannier duality-symmetry in the trotterized critical Ising chain
• Braid group action and quasi-split affine iquantum groups III
• Integrable XYZ spin chain with boundaries
• Quivers with Involutions and Shifted Twisted Yangians via Coulomb Branches
• Dimers for Relativistic Toda Models with Reflective Boundaries
• Kowalevski top revisited
• Boundary quantum phase transitions in the spin-12 Heisenberg chain with boundary magnetic fields
• On quantum group symmetries of conformal field theories
• Quantum Howe duality and Schur duality of type AIII
• New approach to scalar products of Bethe vectors
• Optimal Circuit Size for Fixed-Hamming-Weight Quantum States Preparation
• Modified rational six vertex model on a rectangular lattice : new formula, homogeneous and thermodynamic limits
• An integrable Anderson-impurity problem embedded in the one-dimensional Hubbard model
• Representations of twisted Yangians associated with skew Young diagrams
• Quantum-group-invariant D⁽²⁾_n+1 models: Bethe ansatz and finite-size spectrum
• Solitons, Boundaries, and Quantum Affine Algebras
• Spin fractionalization and zero modes in the spin-(1)/(2) XXZ chain with boundary fields
• On integrability of a q-oscillator lattice with a B-boundary
• On an inverse scattering transform for the nonlinear Schödinger equation on the half-line
• Canonical approach to the WZNW model
• BC-type open SL(2,ℂ) spin chain
• Differential calculus on h-deformed spaces
• Classification of integrable boundary equations for integrable quad-graph systems
• Quantum group symmetry of integrable models on the half-line
• Reflection equation algebras, coideal subalgebras, and their centres
• On domain wall boundary conditions for the XXZ spin Hamiltonian
• Integrable field theory with boundary conditions
• Differential approach to on-shell scalar products in six-vertex models

Related

• On Bäcklund transformations and boundary conditions associated with the quantum inverse problem for a discrete nonlinear integrable system and its connection to Baxter's Q-operator
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