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arXiv · 0910.4029

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

André M. Grabinski·Holger Frahm
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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.

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André M. Grabinski, Holger Frahm. 2009-10-21. Non-diagonal boundary conditions for gl(1|1) super spin chains. https://doi.org/10.1088/1751-8113/43/4/045207

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