Droplet Excitations for the Spin-1/2 XXZ Chain with Kink Boundary Conditions

Bruno Nachtergaele, Spitzer, Wolfgang, Shannon L. Starr

Published Aug 24, 2005• 15 citations

Abstract

We give a precise definition for excitations consisting of a droplet of size n in\n the XXZ chain with various choices of boundary conditions, including kink boundary\n conditions and prove that, for each n, the droplet energies converge to a boundary\n condition independent value in the thermodynamic limit. We rigorously compute an explicit\n formula for this limiting value using the Bethe ansatz.

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OpenAlex

Abstract

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\\alpha_-

\\alpha_+

\\beta_-

\\beta_+

}} are nonzero. A generalization of the Baxter

T-Q

equation that involves more than one independent

Q

is described. We use this solution to compute the boundary energy of the chain in the thermodynamic limit. We conclude the paper with a review of some results for the general integrable boundary terms, where all six boundary parameters are arbitrary.

Thermodynamic limit of the spin-

\frac{1}{2}

XYZ spin chain with the antiperiodic boundary condition

Abstract Based on its off-diagonal Bethe ansatz solution, we study the thermodynamic limit of the spin-

\frac{1}{2}

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.