Non-diagonal boundary conditions for gl(1|1) super spin chains

Abstract

We study a one-dimensional model of free fermions with $\mathfrak{gl}(1|1)$ supersymmetry and demonstrate how non-diagonal boundary conditions can be incorporated into the framework of the graded Quantum Inverse Scattering Method (gQISM) by means of \emph{super matrices} with entries from a superalgebra. For super hermitian twists and open boundary conditions subject to a certain constraint, we solve the eigenvalue problem for the super transfermatrix by means of the graded algebraic Bethe ansatz technique (gABA) starting from a fermionic coherent state. For generic boundary conditions the algebraic Bethe ansatz can not be applied. In this case the spectrum of the super transfer matrix is obtained from a functional relation.

18 pages

References in corpus (4)

• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• Separation of Variables in the open XXX chain
• The XXZ model with anti-periodic twisted boundary conditions
• Spectrum of the supersymmetric t-J model with non-diagonal open boundaries

Cited by in corpus (8)

• Off-diagonal Bethe ansatz and exact solution of a topological spin ring
• Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields
• Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Truncation identities for the small polaron fusion hierarchy
• Bethe Ansatz solution of the small polaron with nondiagonal boundary terms
• Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary
• Fermionic reflection matrices