Modified DMRG algorithm for the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange: Comparison with field theory at large $J_2/J_1$

A modified density matrix renormalization group (DMRG) algorithm is applied to the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange $J_1$, $J_2$ between first and second neighbors. The modified algorithm yields accurate results up to $J_2/J_1 \approx 4$ for the magnetic gap $\Delta$ to the lowest triplet state, the amplitude $B$ of the bond order wave (BOW) phase, the wavelength $\lambda$ of the spiral phase, and the spin correlation length $\xi$. The $J_2/J_1$ dependences of $\Delta$, $B$, $\lambda$ and $\xi$ provide multiple comparisons to field theories of the zigzag chain. The twist angle of the spiral phase and the spin structure factor yield additional comparisons between DMRG and field theory. Attention is given to the numerical accuracy required to obtain exponentially small gaps or exponentially long correlations near a quantum phase transition.