The XXZ model with anti-periodic twisted boundary conditions

Abstract

We derive functional equations for the eigenvalues of the XXZ model subject to anti-diagonal twisted boundary conditions by means of fusion of transfer matrices and by Sklyanin's method of separation of variables. Our findings coincide with those obtained using Baxter's method and are compared to the recent solution of Galleas. As an application we study the finite size scaling of the ground state energy of the model in the critical regime.

arXiv comment22 pages and 3 figures

References in corpus (11)

• Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
• Functional relations and Bethe Ansatz for the XXZ chain
• Exact spectrum of the XXZ open spin chain from the q-Onsager algebra representation theory
• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• Solving the open XXZ spin chain with nondiagonal boundary terms at roots of unity
• Separation of Variables in the open XXX chain
• Q-operator and T-Q relation from the fusion hierarchy
• Exact solution and interfacial tension of the six-vertex model with anti-periodic boundary conditions
• Bethe ansatz for the XXX-S chain with non-diagonal open boundaries
• Exact solution for the spin-$s$ XXZ quantum chain with non-diagonal twists
• Exact solution of the open XXZ chain with general integrable boundary terms at roots of unity

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