Yang-Baxter algebra and generation of quantum integrable models

Abstract

An operator deformed quantum algebra is discovered exploiting the quantum Yang-Baxter equation with trigonometric R-matrix. This novel Hopf algebra along with its $q\to 1$ limit appear to be the most general Yang-Baxter algebra underlying quantum integrable systems. Three different directions of application of this algebra in integrable systems depending on different sets of values of deforming operators are identified. Fixed values on the whole lattice yield subalgebras linked to standard quantum integrable models, while the associated Lax operators generate and classify them in an unified way. Variable values construct a new series of quantum integrable inhomogeneous models. Fixed but different values at different lattice sites can produce a novel class of integrable hybrid models including integrable matter-radiation models and quantum field models with defects, in particular, a new quantum integrable sine-Gordon model with defect.

13 pages, revised and bit expanded with additional explanations, accepted for publication in Theor. Math. Phys

References in corpus (8)

• Algebraic Aspects of Bethe-Ansatz
• Quantum and classical integrable sine-Gordon model with defect
• CONNECTIONS of the LIOUVILLE MODEL and XXZ SPIN CHAIN
• A Simple Lattice Version of the Nonlinear Schrodinger Equation and its Deformation with Exact Quantum Solution
• Aspects of sine-Gordon solitons, defects and gates
• Quantum integrability and Bethe ansatz solution for interacting matter-radiation systems
• Generation of a quantum integrable class of discrete-time or relativistic periodic Toda chains
• Unifying quantization for inhomogeneous integrable models

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• Quantum phase transitions in Bose-Einstein condensates from a Bethe ansatz perspective
• Classical and quantum analysis of a heterotriatomic molecular Bose-Einstein-condensate model
• Exactly solvable models for multiatomic molecular Bose-Einstein condensates
• A bosonic multi-state two-well model
• Exactly solvable models for triatomic-molecular Bose-Einstein Condensates