GAPS IN THE HEISENBERG-ISING MODEL

Details GAPS IN THE HEISENBERG-ISING MODEL GAPS IN THE HEISENBERG-ISING MODEL

1995-03-16

arxiv.org/abs/cond-mat/9503087v1

Physics

Condensed Matter

12 RevTeX pages + 4 figures upon request

Scientific paper

10.1103/PhysRevB.52.1656

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.

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