Persistent currents in open spin chains

H. Frahm^a, J. H. Grelik^a, A. Seel<sup>b

a</sup> Institute of Theoretical Physics, Leibniz University of Hannover
^b Institut für Theoretische Elektrotechnik und Photonik, Universität Siegen, Siegen, Germany

Abstract: Nonparallel boundary magnetic fields can induce a longitudinal (spin) current in a quantum spin chain. We use functional approaches to formulate the spectral problem for the spin-$1/2$ Heisenberg model subject to a class of integrable boundary conditions in terms of an infinite hierarchy of nonlinear integral equations. From these equations, we compute finite-size corrections to the ground-state energy of the antiferromagnetic chain and the induced spin current for a certain range of boundary parameters.

Keywords: integrable spin chain, boundary field, Bethe ansatz, $Y$ system.

Received: 29.04.2011

DOI: 10.4213/tmf6904

 English version: Theoretical and Mathematical Physics, 2012, 171:2, 715–724

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