Free Fermionic Elliptic Reflection Matrices and Quantum Group Invariance

Abstract

Elliptic diagonal solutions for the reflection matrices associated to the elliptic $R$ matrix of the eight vertex free fermion model are presented. They lead through the second derivative of the open chain transfer matrix to an XY hamiltonian in a magnetic field which is invariant under a quantum deformed Clifford--Hopf algebra.

9 pages, Latex

References in corpus (4)

• Addendum to ``Integrability of Open Spin Chains with Quantum Algebra Symmetry''
• A Two Parameter Deformation of the SU(1/1) Superalgebra and the XY Quantum Chain in a Magnetic Field
• New Solutions to the Yang--Baxter Equation from Two--Dimensional Representations of $U_q(sl(2))$ at Roots of Unit
• On Integrable Quantum Group Invariant Antiferromagnets

Cited by in corpus (15)

• Boundary K-matrices for the XYZ, XXZ AND XXX spin chains
• Integrable open-boundary conditions for the supersymmetric t-J model. The quantum group invariant case
• Bethe Ansatz solution of the open XX spin chain with nondiagonal boundary terms
• The Highest Weight Property for the $S{U}_q(n)$ Invariant Spin Chains
• Integrability of the $D_n^2$ vertex models with open boundary
• Surface Critical Phenomena and Scaling in the Eight-Vertex Model
• Lattice regularisation of a non-compact boundary conformal field theory
• Classification of Solutions to Reflection Equation of Two-Component Systems
• Supersymmetric Sine-Gordon Model and the Eight-Vertex Free Fermion model with Boundary
• D_{n+1}^(2) Reflection K-matrices
• Integrability of open boundary driven quantum circuits
• Fateev-Zamolodchikov and Kashiwara-Miwa models: boundary star-triangle relations and surface critical properties
• Four State Models and Clifford Algebras
• Two Magnetic Impurities with Arbitrary Spins in Open Boundary t-J Model
• The spectrum of an open vertex model based on the U_q[SU(2)] at roots of unity