Classifying integrable spin-1/2 chains with nearest neighbour interactions

Abstract

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 between solutions of the Yang-Baxter equation and the graded Yang-Baxter equation which extends our results to the graded two-dimensional case.

arXiv commentPublished version

References in corpus (15)

• Remarks on the notion of quantum integrability
• Integrability of Conformal Fishnet Theory
• Lectures on Yangian Symmetry
• Integrability Test for Spin Chains
• Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters
• The low-energy limit of AdS${}_3$/CFT${}_2$ and its TBA
• Ladder operator for the one-dimensional Hubbard model
• Algebraic Bethe ansatz for the quantum group invariant open XXZ chain at roots of unity
• Solving and classifying the solutions of the Yang-Baxter equation through a differential approach. Two-state systems
• On the solutions of the Yang-Baxter equations with general inhomogeneous eight-vertex $R$-matrix: Relations with Zamolodchikov's tetrahedral algebra
• The Jordan Structure of Two Dimensional Loop Models
• The One-Loop Spectral Problem of Strongly Twisted $\mathcal{N}$=4 Super Yang-Mills Theory
• Integrable Deformations of the XXZ Spin Chain
• Quantum Inverse Scattering Method with anyonic grading
• Massless $Ad{S}_2$ scattering and Bethe ansatz

Cited by in corpus (28)

• Constructing Integrable Lindblad Superoperators
• Yang-Baxter and the Boost: splitting the difference
• Classifying nearest-neighbour interactions and deformations of AdS
• Integrable hard rod deformation of the Heisenberg spin chains
• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension
• Introduction to classical and quantum integrability
• Quantum many-body scars in spin models with multibody interactions
• Integrable nonunitary quantum circuits
• Integrable spin chains and the Clifford group
• Free fermions beyond Jordan and Wigner
• Integrable spin chains and cellular automata with medium range interaction
• 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
• Complete classification of integrability and non-integrability of S=1/2 spin chains with symmetric next-nearest-neighbor interaction
• Algebraic classification of Hietarinta's solutions of Yang-Baxter equations~:~invertible $4\times 4$ operators
• Unveiling chiral states in the XXZ chain: Finite-size scaling probing symmetry-enriched $c=1$ conformal field theories
• Baxterisation of the fused Hecke algebra and R-matrices with gl(N)-symmetry
• Jordan blocks and the Bethe ansatz II: The eclectic spin chain beyond $K=1$
• Lifting integrable models and long-range interactions
• Solutions to the constant Yang-Baxter equation in all dimensions
• Non-hermitian integrable systems from constant non-invertible solutions of the Yang-Baxter equation
• Integrable models on Rydberg atom chains
• Jordan blocks and the Bethe ansatz III: Class 5 model and its symmetries
• Dichotomy theorem separating complete integrability and non-integrability of isotropic spin chains
• Integrability from a single conservation law in quantum spin chains
• Flag Integrable Models and Generalized Graded Algebras
• An integrable deformed Landau-Lifshitz model with particle production?
• All 4 x 4 solutions of the quantum Yang-Baxter equation