Numerical method for detecting incommensurate correlations in the Heisenberg zigzag ladder

We study two Heisenberg spin-1/2 chains coupled by a frustrating “zigzag” interaction. We are particularly interested in the regime of weak interchain coupling, which is difficult to analyze by either numerical or analytical methods. Previous density matrix renormalization-group studies of the isotropic model with open boundary conditions and sizable interchain coupling have established the presence of incommensurate correlations and of a spectral gap. By using twisted boundary conditions with an arbitrary twist angle, we are able to determine the incommensurabilities both in the isotropic case and in the presence of an exchange anisotropy by means of exact diagonalization of relatively short finite chains of up to $24$ sites. Using twisted boundary conditions results in a very smooth dependence of the incommensurabilities on system size, which makes the extrapolation to infinite systems significantly easier than for open or periodic chains.