Spontaneous dimerization in the $S=\frac{1}{2}$ Heisenberg antiferromagnetic chain with competing interactions

Spontaneous dimerization is found in the $S=\frac{1}{2}$ isotropic Heisenberg antiferromagnetic chain with competing nearest- and next-nearest-neighbor exchange, $\frac{J_2}{J_1}\gtrsim \frac{1}{6}$, and results from the same umklapp processes that lead to the Néel state when easy-axis exchange anisotropy is present. Spontaneous and externally induced dimerizations are contrasted.