Abstract
Based on its off-diagonal Bethe ansatz solution, we study the thermodynamic limit of the spin- frac{1}{2} XYZ spin chain with the antiperiodic boundary condition. The key point of our method is that there exist some degenerate points of the crossing parameter ηm,l, at which the associated inhomogeneous T − Q relation becomes a homogeneous one. This makes extrapolating the formulae deriving from the homogeneous one to an arbitrary η with O(N−2) corrections for a large N possible. The ground state energy and elementary excitations of the system are obtained. By taking the trigonometric limit, we also give the results of antiperiodic XXZ spin chain within the gapless region in the thermodynamic limit, which does not have any degenerate points.
Highlights
Chain with arbitrary number of sites is obtained [11, 12], where the eigenvalue of transfer matrix is given by an inhomogeneous T − Q relation
We study the thermodynamic limit of the anisotropic spinspin chain with the antiperiodic boundary condition described by the Hamiltonian (2.1) and (2.3) based on its off-diagonal Bethe ansatz solution
We overcome the difficult that it is hard to take the thermodynamic limit of the associated BAEs deriving from its inhomogeneous T − Q relation
Summary
Let us fix a generic complex number η and a generic imaginary number τ such that Im(τ ) >. QYBE (2.6) and the Z2-symmetry (2.7) lead to that the transfer matrices with different spectral parameters are mutually commutative [1, 2], i.e., [t(u), t(v)] = 0, which guarantees the integrability of the model by treating t(u) as the generating functional of the conserved quantities. Many attempts have been done to solve the resulting BAEs from inhomogeneous T − Q relations [17,18,19,20,21,22], the corresponding distributions of Bethe roots for groundstate or elementary excitation states is still an interesting open problem This motivates us in this paper to look for another way, instead of solving the BAEs (2.13) for a large N , to the antiperiodic boundary condition
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