arXiv:0910.4029 · Journal of Physics A Mathematical and Theoretical

Non-diagonal boundary conditions for \mathfrak {gl}(1|1) super spin chains

André M Grabinski, Holger Frahm

Published Jan 4, 2010• 16 citations

Abstract

We study a one-dimensional model of free fermions with 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 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 cannot be applied. In this case the spectrum of the super transfermatrix is obtained from a functional relation.

DOI: 10.1088/1751-8113/43/4/045207

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