Yang-Baxter and the Boost: splitting the difference

Abstract

In this paper we continue our classification of regular solutions of the Yang-Baxter equation using the method based on the spin chain boost operator developed in \cite{deLeeuw:2019zsi}. We provide details on how to find all non-difference form solutions and apply our method to spin chains with local Hilbert space of dimensions two, three and four. We classify all $16\times 16$ solutions which exhibit $\mathfrak{su}(2)\oplus \mathfrak{su}(2)$ symmetry, which include the one-dimensional Hubbard model and the $S$-matrix of the ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ superstring sigma model. In all cases we find interesting novel solutions of the Yang-Baxter equation.

References in corpus (44)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Review of AdS/CFT Integrability: An Overview
• The su(2|2) Dynamic S-Matrix
• Foundations of the AdS_5 x S^5 Superstring. Part I
• The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
• The Analytic Bethe Ansatz for a Chain with Centrally Extended su(2|2) Symmetry
• Quantum Deformations of the One-Dimensional Hubbard Model
• The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux
• The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
• The Yangian symmetry of the Hubbard Model
• All-loop worldsheet S matrix for AdS_3 x S^3 x T^4
• Yang-Baxter integrable models in experiments: from condensed matter to ultracold atoms
• Lectures on Yangian Symmetry
• Integrability Test for Spin Chains
• A Quantum Affine Algebra for the Deformed Hubbard Chain
• Classifying nearest-neighbour interactions and deformations of AdS
• Integrable S-matrices, massive and massless modes and the AdS_2 x S^2 superstring
• Classifying integrable spin-1/2 chains with nearest neighbour interactions
• Ladder operator for the one-dimensional Hubbard model
• Solving and classifying the solutions of the Yang-Baxter equation through a differential approach. Two-state systems
• The ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$ worldsheet S matrix
• On the solutions of the Yang-Baxter equations with general inhomogeneous eight-vertex $R$-matrix: Relations with Zamolodchikov's tetrahedral algebra
• The Bound State S-matrix of the Deformed Hubbard Chain
• Symmetries of spin systems and Birman-Wenzl-Murakami algebra
• Quantum Inverse Scattering and the Lambda Deformed Principal Chiral Model
• Spectral Decomposition and Baxterisation of Exotic Bialgebras and Associated Noncommutative Geometries
• On the solutions to the multi-parametric Yang-Baxter equations
• The Yang-Baxter equation for PT invariant nineteen vertex models
• R-matrices of three-state Hamiltonians solvable by Coordinate Bethe Ansatz
• Integrability and duality in spin chains
• Classification of three-state Hamiltonians solvable by Coordinate Bethe Ansatz
• Integrable three-state vertex models with weights lying on genus five curves
• Something interacting and solvable in 1d
• A new braid-like algebra for Baxterisation
• Boost generator in AdS_3 integrable superstrings for general braiding
• The twisted story of worldsheet scattering in $\eta$-deformed $Ad{S}_5\times S^5$
• Fifteen-vertex models with non-symmetric $R$ matrices
• 3-state Hamiltonians associated to solvable 33-vertex models
• Baxterisation of the fused Hecke algebra and R-matrices with gl(N)-symmetry
• An Integrable Nineteen Vertex Model Lying on a Hypersurface
• The factorized F-matrices for arbitrary U(1)^(N-1) integrable vertex models
• New R-matrices with non-additive spectral parameters and integrable models of strongly correlated fermions
• Quantum entanglement, supersymmetry, and the generalized Yang-Baxter equation

Cited by in corpus (21)

• Constructing Integrable Lindblad Superoperators
• Introduction to classical and quantum integrability
• Generalised Onsager Algebra in Quantum Lattice Models
• Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices
• Integrable deformations of AdS/CFT
• Integrable spin chains and cellular automata with medium range interaction
• Integrability of open boundary driven quantum circuits
• Jordan blocks and the Bethe ansatz I: The eclectic spin chain as a limit
• The solutions of the Yang-Baxter equation for the $(n+1)(2n+1)$-vertex models through a differential approach
• Unveiling chiral states in the XXZ chain: Finite-size scaling probing symmetry-enriched $c=1$ conformal field theories
• A study of integrable form factors in massless relativistic AdS_3
• Lifting integrable models and long-range interactions
• Jordan blocks and the Bethe ansatz II: The eclectic spin chain beyond $K=1$
• Integrable models on Rydberg atom chains
• Integrability and charge transport in asymmetric quantum-circuit geometries
• Jordan blocks and the Bethe ansatz III: Class 5 model and its symmetries
• Integrability from a single conservation law in quantum spin chains
• Dichotomy theorem separating complete integrability and non-integrability of isotropic spin chains
• Flag Integrable Models and Generalized Graded Algebras
• A study of integrable form factors in massless relativistic $Ad{S}_2$
• All 4 x 4 solutions of the quantum Yang-Baxter equation