Scaling Property of the F–AF Spin Chain Near the Exactly Solvable Point

概要

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We investigate the ground state of the $J_{1}$–$J_{2}$ spin-1/2 chain with $J_{1}<0$ and $J_{2}>0$ in the case that the nearest-neighbor $J_{1}$ interaction in the $z$-direction has a weak anisotropy as $J_{1}(1-\alpha)$. We perform a perturbational analysis for small $\alpha$ and $\lambda\equiv J_{2}-|J_{1}|/4$ with the exact solution of the unperturbed ground state for $\alpha=\lambda=0$. The scaling property of the ground-state energy is examined in detail. By the numerical diagonalization analysis of finite-size systems, we found the phase boundary equation between the spin fluid and dimer phases as $\alpha_{\text{c}}=14\lambda_{\text{c}}^{4/3}$.
2010-04-15