Melting of a frustration-induced dimer crystal and incommensurability in the J_1-J_2 two-leg ladder

TL;DR

This paper investigates the phase diagram of a frustrated two-leg ladder model, revealing an Ising transition, incommensurability effects, and connections to experimental compounds, using numerical and analytical methods.

Contribution

It provides a comprehensive analysis of the phase transitions and incommensurability in a frustrated J_1-J_2 ladder, bridging chain and ladder physics with new insights.

Findings

Identified an Ising transition between dimer and rung-singlet phases.

Discovered incommensurability in spin correlations due to frustration.

Analyzed the evolution of incommensurability from chain to ladder limit.

Abstract

The phase diagram of an antiferromagnetic ladder with frustrating next-nearest neighbor couplings along the legs is determined using numerical methods (exact diagonalization and density-matrix renormalization group) supplemented by strong-coupling and mean-field analysis. Interestingly, this model displays remarkable features, bridging the physics of the J_1-J_2 chain and of the unfrustated ladder. The phase diagram as a function of the transverse coupling J_{\perp} and the frustration J_2 exhibits an Ising transition between a columnar phase of dimers and the usual rung-singlet phase of two-leg ladders. The transition is driven by resonating valence bond fluctuations in the singlet sector while the triplet spin gap remains finite across the transition. In addition, frustration brings incommensurability in the real-space spin correlation functions, the onset of which evolves smoothly from the J_1-J_2 chain value to zero in the large-J_{\perp} limit. The onset of incommensurability in the spin structure-factor and in the dispersion relation is also analyzed. The physics of the frustrated rung-singlet phase is well understood using perturbative expansions and mean-field theories in the large-J_{\perp} limit. Lastly, we discuss the effect of the non-trivial magnon dispersion relation on the thermodynamical properties of the system. The relation of this model and its physics to experimental observations on compounds which are currently investigated, such as BiCu_2PO_6, is eventually addressed.