Excited states in the twisted XXZ spin chain

Abstract

We compute the finite size spectrum for the spin 1/2 XXZ chain with twisted boundary conditions, for anisotropy in the regime $0<\gamma <\pi /2$, and arbitrary twist $\theta$. The string hypothesis is employed for treating complex excitations. The Bethe Ansatz equtions are solved within a coupled non-linear integral equation approach, with one equation for each type of string. The root-of-unity quantum group invariant periodic chain reduces to the XXZ_1/2 chain with a set of twist boundary conditions ($\pi /\gamma \in Z$, $\theta$ an integer multiple of $\gamma$). For this model, the restricted Hilbert space corresponds to an unitary conformal field theory, and we recover all primary states in the Kac table in terms of states with specific twist and strings.

16 pages, Latex; added discussion on quantum group invariance and arbitrary magnon number

References in corpus (1)

• Non linear integral equation and excited--states scaling functions in the sine-Gordon model

Cited by in corpus (4)

• Bosonization with a background $U(1)$ gauge field
• The anticommutator spin algebra, its representations and quantum group invariance
• Kubo's response theory and bosonization with a background gauge field and irrelevant perturbations
• Spin fractionalization and zero modes in the spin-$\frac{1}{2}$ XXZ chain with boundary fields