Melting of a frustration-induced dimer crystal and incommensurability in theJ1-J2two-leg ladder

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 J1-J2 chain and of the unfrustated ladder. The phase diagram as a function of the transverse coupling J ⊥ and the frustration 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-J2 chain value to zero in the large-J ⊥ 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 ⊥ 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 BiCu2PO6, is eventually addressed.PACS numbers: 75.10. Kt, 75.40.Mg, 75.10.Jm, 75.10.Pq Ladder materials offer a unique playground to improve our understanding of the subtleties arising from quantum effects in low dimensional geometries. 1 For antiferromagnetic S = 1/2 Heisenberg models, it is well-known that ladders with an even number of legs n ℓ display short-range correlations for any non-zero inter-chain coupling J ⊥ and a finite spin gap ∆ s ∼ J ⊥ exp(−an ℓ ), whereas the gapless quasi-long-range ordered state of a single S = 1/2 chain is robust for ladders having an odd number of legs. 2 Ladder physics has been intensively explored during the last two decades both theoretically and experimentally, in particular regarding spin gap physics, impurity effects, 3 field-induced magnetization processes, 4 superconductivity in hole doped systems, 1 etc. Despite their rather simple geometry and the huge amount of studies, ladder systems remain a topic of current interest. Newly synthesized two-leg ladder materials which exhibit sizable spin gaps ∼ 1 meV have recently emerged, 4,5 thus opening the possibility to close the gap with an external magnetic field.The ground-state of a spin-1/2 Heisenberg two-leg ladder is a genuine quantum state which has no classical analog. Schematically, the short-range nature of the spin correlations can be encoded in the so-called resonating valence bond (RVB) picture with short range pairwise singlet bonds fluctuating over a few lattice sites. 6 Such a state, sometimes called "rung-singlet" (RS) because the strongest antiferromagnetic correlations are a...

Coupled spin- 12 ladders as microscopic models for non-Abelian chiral spin liquids

“…21 and Lavarélo et al in Ref. 22 have also shown numerically that two other families of ladders for quantum spin-1/2 display a quantum critical point in the Ising universality class that separates two distinct gapped dimer phases [23]. We note as well that quantum spin-1 chains can also show a quantum critical point in the Ising universality class separating gapped phases that are not related by a loss of symmetry [24].…”

“…The entanglement entropy computed with DMRG also agrees with that of the Ising universality class. If we cut open the two-leg ladder of length N along a rung into one block of size x, the entanglement entropy S(x, N ) scales with x and N like [22,[29][30][31][32][33] S(x, N ) = c 6 ln…”

“…As in Ref. 22, we plot the groundstate expectation value for the leg-dimer order parameters in Fig. 2(a) as a function of J ∨ for different system sizes, together with an extrapolation to the thermodynamic limit, which allows us to locate the transition at the point J ∨ ≈ J 2 ≈ 0.44 [27].…”

Lifshitz Transition Induced by Magnetic Field in Frustrated Two-Leg Spin-Ladder Systems

“…Since the magnetic behaviors in the rung-singlet phase belong to the same universality class in this limit, the strong rung-coupling limit can be justified qualitatively. In this limit, the BOMF approximation [3,4,11] works well and the low-energy physics can be described by a hard-core boson (triplon). Then, the Hamiltonian of spin-1/2 operators (1) can be rewritten as follows,…”

“…[9,10] In this model, there are two possibilities of the ground-state phase without applied magnetic fields: the columnar-dimer and the rung-singlet phases. The previous works have claimed that the real compound is located in the rung-singlet phase similar to that of non-frustrated 2LSL [11][12][13]. In this phase, two spins on a rung become a singlet pair and the elementary excitation is described by a hard-core boson of a triplet pair on a rung, "triplon".…”