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arXiv:1107.5498 · Physical Review B

Melting of a frustration-induced dimer crystal and incommensurability in the J1 - J2 two-leg ladder

Arthur Lavarélo, Guillaume Roux, Nicolas Laflorencie

Published Oct 4, 2011• 42 citations
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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 unfrustrated ladder. The phase diagram as a function of the transverse coupling ${J}_{\ensuremath{\perp}}$ 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-${J}_{\ensuremath{\perp}}$ 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-${J}_{\ensuremath{\perp}}$ limit. Last, we discuss the effect of the nontrivial magnon dispersion relation on the thermodynamical properties of the system. The relation of this model and its physics to experimental observations on compounds that are currently investigated, such as BiCu${}_{2}$PO${}_{6}$, is eventually addressed.

DOI
10.1103/physrevb.84.144407

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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 J1{J}_{1}J1​-J2{J}_{2}J2​ chain and of the unfrustrated ladder. The phase diagram as a function of the transverse coupling J\ensuremath⊥{J}_{\ensuremath{\perp}}J\ensuremath⊥​ and the frustration J2{J}_{2}J2​ 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 J1{J}_{1}J1​-J2{J}_{2}J2​ chain value to zero in the large-J\ensuremath⊥{J}_{\ensuremath{\perp}}J\ensuremath⊥​ 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\ensuremath⊥{J}_{\ensuremath{\perp}}J\ensuremath⊥​ limit. Last, we discuss the effect of the nontrivial magnon dispersion relation on the thermodynamical properties of the system. The relation of this model and its physics to experimental observations on compounds that are currently investigated, such as BiCu2{}_{2}2​PO6{}_{6}6​, is eventually addressed.
We investigate a spin-1/21/21/2 two-leg honeycomb ladder with frustrating next-nearest-neighbor (NNN) coupling along the legs, which is equivalent to two ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ spin chains coupled with ${J}_{\ensuremath{\perp}}$ at odd rungs. The full parameter region of the model is systematically studied using conventional and infinite density-matrix renormalization group as well as bosonization. The rich phase diagram consists of five distinct phases: a Haldane phase, a NNN-Haldane phase, and a staggered dimer phase when ${J}_{\ensuremath{\perp}}<0$; a rung singlet phase and a columnar dimer phase when ${J}_{\ensuremath{\perp}}>0$. An interesting reentrant behavior from the dimerized phase into the Haldane phase is found as the frustration J2{J}_{2}J2​ increases. The universalities of the critical phase transitions are fully analyzed. Phase transitions between dimerized and disordered phases belong to the two-dimensional Ising class with a central charge c=1/2c=1/2c=1/2. The transition from the Haldane phase to NNN-Haldane phase is of a weak topological first order, while the continuous transition between the Haldane phase and rung singlet phase has a central charge c=2c=2c=2.
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