Unified algebraic Bethe ansatz for two-dimensional lattice models

Abstract

We develop a unified formulation of the quantum inverse scattering method for lattice vertex models associated to the non-exceptional $A_{2r}^{(2)}$, $A_{2r-1}^{(2)}$, $B_r^{(1)}$, $C_r^{(1)}$, $D_{r+1}^{(1)}$ and $D_{r+1}^{(2)}$ Lie algebras. We recast the Yang-Baxter algebra in terms of novel commutation relations between creation, annihilation and diagonal fields. The solution of the $D_{r+1}^{(2)}$ model is based on an interesting sixteen-vertex model which is solvable without recourse to a Bethe ansatz.

plain latex, 9 pages

References in corpus (3)

• The Quantum Inverse Scattering Method for Hubbard-like Models
• The algebraic Bethe ansatz for rational braid-monoid lattice models
• U(N) Matrix Difference Equations and a Nested Bethe Ansatz

Cited by in corpus (16)

• R-matrices and Spectrum of Vertex Models based on Superalgebras
• Algebraic Bethe ansatz for the one-dimensional Hubbard model with open boundaries
• Phase Diagram of an Integrable Alternating $U_q[sl(2|1)]$ Superspin Chain
• Integrability of the $D_n^2$ vertex models with open boundary
• New R-matrices from Representations of Braid-Monoid Algebras based on Superalgebras
• Algebraic Bethe Ansatz for U(1) Invariant Integrable Models: The Method and General Results
• The algebraic Bethe ansatz for open vertex models
• Spectrum of the quantum integrable $D_2^{(2)}$ spin chain with generic boundary fields
• On the multiparametric {\cal U}_q[D_{n+1}^{(2)}] vertex model
• Exactly Solvable Models of Interacting Spin-s Particles in one-dimension
• Integrable variant of the one-dimensional Hubbard model
• Algebraic Bethe ansatz for 19-vertex models with upper triangular K-matrices
• The $D_3^{(2)}$ spin chain and its finite-size spectrum
• On the algebraic Bethe ansatz: Periodic boundary conditions
• Exact physical quantities of the $D_2^{(2)}$ spin chain model with generic open boundary conditions
• Factorization identities and algebraic Bethe ansatz for $D_2^{(2)}$ models