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

TL;DR

This paper investigates the phase diagram of a frustrated two-leg Heisenberg ladder with additional rung spins, revealing a frustration-driven spin-Peierls transition and a critical phase with a spinon continuum.

Contribution

It provides a combined numerical and analytical study of the zero-temperature phases in a frustrated ladder model, including dynamical spin structure factors and the decoupling of rung spins.

Findings

Strong rung coupling leads to a gapped dimerized phase.

Weak rung coupling results in a critical phase with a spinon continuum.

Rung spins decouple when their coupling drops below the leg coupling.

Abstract

We study the antiferromagnetic spin-half Heisenberg ladder in the presence of an additional frustrating rung spin which is motivated and relevant also for the description of real two-dimensional materials such as the two-dimensional trimer magnet Ba$_4$Ir$_3$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 which renders the system critical overall. In either case, the additional rung spin quickly get sidelined and nearly decouple once their bare coupling to the ladder drops somewhat below the direct Heisenberg coupling of the legs.