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Nuclear Physics B

Exact solution of XXZ spin chain with unparallel boundary fields

Junpeng Cao, Hai-Qing Lin, Kangjie Shi, Yupeng Wang

Published May 28, 2003• 244 citations
Publisher
DOI
10.1016/s0550-3213(03)00372-9

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By using a set of gauge transformations, the exact solutions of the XXZ spin chain with unparallel boundary magnetic fields are derived in the framework of the algebraic Bethe ansatz. In the easy-plane case, we show the elementary excitations are some kind of spinons without definite spin because the U(1) symmetry is broken, while in the easy-axis ferromagnetic case a spiral state is realized in the ground state. The correlation functions, the spin torque as well as the spin voltage for the later case are also derived.
Abstract The thermodynamic properties of the XXZ spin chain with integrable open boundary conditions at the gaped region (i.e. the anisotropic parameter being a real number) are investigated. It is shown that the contribution of the inhomogeneous term in the T − Q relation of the ground state and elementary excited state can be neglected when the size of the system N tends to infinity. The surface energy and elementary excitations induced by the unparallel boundary magnetic fields are obtained.
Abstract In this paper we continue our derivation of the correlation functions of open quantum spin 1/2 chains with unparallel magnetic fields on the edges; this time for the more involved case of the XXZ spin 1/2 chains. We develop our study in the framework of the quantum separation of variables, which gives us both the complete spectrum characterization and simple scalar product formulae for separate states, including transfer matrix eigenstates. Here, we leave the boundary magnetic field in the first site of the chain completely arbitrary, and we fix the boundary field in the last site N of the chain to be a specific value along the z -direction. This is a natural first choice for the unparallel boundary magnetic fields. We prove that under these special boundary conditions, on the one side, we have a simple enough complete spectrum description in terms of homogeneous Baxter like TQ -equation. On the other side, we prove a simple enough description of the action of a basis of local operators on transfer matrix eigenstates as linear combinations of separate states. Thanks to these results, we achieve our main goal to derive correlation functions for a set of local operators both for the finite and half-infinite chains, with multiple integral formulae in this last case.