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The quantum phases of one-dimensional spin $s= 1/2$ chains are discussed formodels with two parameters, frustrating exchange $g = J_2 > 0$ between secondneighbors and normalized nonfrustrating power-law exchange with exponent$\alpha$ and distance dependence $r^{-\alpha}$. The ground state (GS) at $g =0$ has long-range order (LRO) for $\alpha < 2$, long-range spin fluctuationsfor $\alpha > 2$. The models conserve total spin $S = S_A + S_B$, have singletGS for any $g$, $\alpha \ge 0$ and decouple at $1/g = 0$ to linear Heisenbergantiferromagnets on sublattices $A$ and $B$ of odd and even-numbered sites.Exact diagonalization of finite chains gives the sublattice spin $ \ < S^2_A \>$, the magnetic gap $E_m$ to the lowest triplet state and the excitation$E_{\sigma}$ to the lowest singlet with opposite inversion symmetry to the GS.An analytical model that conserves sublattice spin has a first order quantumtransition at $g_c = 1/4{\rm ln2}$ from a GS with perfect LRO to a decoupledphase with $S_A = S_B = 0$ for $g \ge 4/\pi^2$ and no correlation between spinsin different sublattices. The model with $\alpha = 1$ has a first ordertransition to a decoupled phase that closely resembles the analytical model.The bond order wave (BOW) phase and continuous quantum phase transitions offinite models with $\alpha \ge 2$ are discussed in terms of GS degeneracy where$E_{\sigma}(g) = 0$, excited state degeneracy where $E_{\sigma}(g) = E_m(g)$,and $\ < S^2_A \ >$. The decoupled phase at large frustration has nondegenerateGS for any exponent $\alpha$ and excited states related to sublatticeexcitations.

Decoupled phase of frustrated spin-1/2 antiferromagnetic chains with and without long range order in the ground state