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

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

2010-03-25

arxiv.org/abs/1003.4804v1

Physics

Condensed Matter

Strongly Correlated Electrons

15 pages, 10 figures

Scientific paper

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 $\alpha_{\rm c} = 14 \lambda_{\rm c}^{4/3}$.

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