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978-3-8439-2161-9, Reihe Physik

Jan-Henryk Grelik Boundary Effects and Magnetic Impurities in Heisenberg Chains

105 Seiten, Dissertation Universität Hannover (2015), Hardcover, B5

This thesis presents exact results of Heisenberg spin chains with impurities and general boundary conditions. The corresponding Hamiltonians are constructed within the framework of the Quantum Inverse Scattering Method which provides a family of commuting operators. Sklyanin's technique for the construction of open chains is applied and the resulting integrable quantum models are solved by means of different Bethe ansatz methods.

The algebraic Bethe ansatz leads to a set of Bethe equations which are transformed into integral equations in the thermodynamic limit. The integral equations describe bulk properties as well as surface and impurity properties of the chain individually. A bulk magnetic field, acting on all spins of the chain, drives a magnetization which is calculated for weak bulk magnetic field strengths by an approximative Wiener-Hopf approach. These calculations show interesting features of strongly correlated quantum systems, e.g. finite surface and impurity magnetizations for vanishing magnetic fields.

In case of non-diagonal boundary conditions an important prerequisite of the algebraic Bethe ansatz is not satisfied and different approaches need to be considered, e.g. functional methods. These techniques yield for the corresponding Heisenberg chain an infinite hierarchy of non-linear integral equations, the so-called Y-system, which is solved numerically. Certain configurations of the boundary parameters induce a persistent current in the spin chain which is calculated by means of a modified Y-system.