Dimerization and spin decoupling in a two-leg Heisenberg ladder with frustrated trimer rungs

Abstract

We study the antiferromagnetic spin-half Heisenberg ladder in the presence of an additional frustrating rung spin that is motivated and relevant also for the description of real two-dimensional materials such as the two-dimensional trimer magnet ${\mathrm{Ba}}_{4}{\mathrm{Ir}}_{3}{\mathrm{O}}_{10}$. We study the zero-temperature phase diagram, where we combine numerical and analytical methods into an overall consistent description. All numerical simulations are also accompanied by studies of the dynamical spin structure factor obtained via the density matrix renormalization group. Overall, we find in the regime of strong rung coupling a gapped dimerized phase related to competing symmetry sectors in Hilbert space that ultimately results in frustration-driven spin-Peierls transition. In the weak rung-coupling regime, the system is uniform yet shows a gapped spinon continuum together with a sharp coherent low-energy branch that renders the system critical overall. In either case, the additional rung spin quickly gets sidelined and nearly decouples once its bare coupling to the ladder drops somewhat below the direct Heisenberg coupling of the legs.