GAPS IN THE HEISENBERG-ISING MODEL

Abstract

We report on the closing of gaps in the ground state of the critical Heisenberg-Ising chain at momentum $\pi$. For half-filling, the gap closes at special values of the anisotropy $\Delta =\cos (\pi /Q)$, $Q$ integer. We explain this behavior with the help of the Bethe Ansatz and show that the gap scales as a power of the system size with variable exponent depending on $\Delta$. We use a finite-size analysis to calculate this exponent in the critical region, supplemented by perturbation theory at $\Delta \sim 0$. For rational $1/r$ fillings, the gap is shown to be closed for {\em all} values of $\Delta$ and the corresponding perturbation expansion in $\Delta$ shows a remarkable cancellation of various diagrams.

12 RevTeX pages + 4 figures upon request

References in corpus (2)

• Exiton, Spinon and Spin Wave Modes in an Exactly Soluble One-Dimensional Quantum Many-Body System
• Twisted Boundary Conditions and the Adiabatic Ground State for the Attractive XXZ Luttinger Liquid

Cited by in corpus (8)

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• Spectral flow of non-hermitian Heisenberg spin chain with complex twist
• Adiabatic Ground-State Properties of Spin Chains with Twisted Boundary Conditions
• Excited states in the twisted XXZ spin chain
• Bloch oscillations in the spin-1/2 XXZ chain