ISBN 9783843912785

978-3-8439-1278-5, Reihe Physik

André Markus Grabinski
Functional Bethe Ansatz Methods for the Exact Solution of Integrable Super Spin Chains with Non-Diagonal Boundary Fields

103 Seiten, Dissertation Universität Hannover (2013), Hardcover, B5

Zusammenfassung / Abstract

This thesis addresses the exact solution of the small polaron model, a one-dimensional integrable quantum system of interacting spinless fermions. Within the framework of a graded Quantum Inverse Scattering Method (QISM), the model is considered with periodic as well as with general open boundary conditions. Due to the fermionic nature of the small polaron model, the latter case requires the presence of Grassmann valued boundary fields in those terms breaking the U(1) bulk symmetry. Similar to the situation for ungraded models, the existence of such non-diagonal (i.e. particle number changing) contributions confronts the applicability of algebraic Bethe ansatz methods with the problem of finding a suitable reference state. In contrast to the case of free fermions it is in no way obvious how such a reference state might look like or how it can be constructed. Thus, alternative approaches based on functional methods are considered which circumvent this issue.