Nested Bethe ansatz for `all' open spin chains with diagonal boundary conditions

Abstract

We present in an unified and detailed way the nested Bethe ansatz for open spin chains based on Y(gl(\fn)), Y(gl(\fm|\fn)), U_{q}(gl(\fn)) or U_{q}(gl(\fm|\fn)) (super)algebras, with arbitrary representations (i.e. `spins') on each site of the chain and diagonal boundary matrices (K^+(u),K^-(u)). The nested Bethe anstaz applies for a general K^-(u), but a particular form of the K^+(u) matrix. The construction extends and unifies the results already obtained for open spin chains based on fundamental representation and for some particular super-spin chains. We give the eigenvalues, Bethe equations and the form of the Bethe vectors for the corresponding models. The Bethe vectors are expressed using a trace formula.

40 pages; examples of Bethe vectors added; Bethe equations for U_q(gl(2/2)) added; misprints corrected

References in corpus (4)

• Bethe eigenvectors of higher transfer matrices
• Exact solutions and elementary excitations in the XXZ spin chain with unparallel boundary fields
• Out-of-equilibrium relaxation of the Edwards-Wilkinson elastic line
• New results in the XXZ open spin chain

Cited by in corpus (23)

• The half-infinite XXZ chain in Onsager's approach
• Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions
• The open XXX spin chain in the SoV framework: scalar product of separate states
• Algebraic Bethe ansatz for open XXX model with triangular boundary matrices
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• Generalized coordinate Bethe ansatz for non diagonal boundaries
• Preparing exact eigenstates of the open XXZ chain on a quantum computer
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• Solutions of ${\mathfrak{gl}}_{m|n}$ XXX Bethe ansatz equation and rational difference operators
• Diagonalization of transfer matrix of supersymmetry $u_q(\widehat{sl}(m+1|n+1))$ chain with a boundary
• On Separation of Variables for Reflection Algebras
• Nested Bethe ansatz for Y(gl(n)) open spin chains with diagonal boundary conditions
• On the supersymmetric XXX spin chains associated to ${\mathfrak{gl}}_{1|1}$
• Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains
• On boundary super algebras
• Eigenvalues of quantum Gelfand invariants
• Nested algebraic Bethe ansatz for open spin chains with even twisted Yangian symmetry
• Scattering matrix for a general gl(2) spin chain
• Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary
• Twisted super Yangians of type AIII and their representations
• Central elements and evaluation map for the quantum queer superalgebras
• Fermionic reflection matrices