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...
The magnetic responses of a spin-1/2 ladder doped with non-magnetic impurities are studied combining both analytical and numerical methods. The regime where frustration induces incommensurability is taken into account. Several improvements are made on the results of the seminal work by A. Furusaki, J. Phys. Soc. Jpn., 65, 2385 (1996)], and deviations from the Brillouin magnetization curve due to interactions are also analyzed. We first discuss the magnetic profile around a single impurity and the effective interactions between impurities within the bond-operator mean-field theory. The results are compared to density-matrix renormalization group calculations. In particular, these quantities are shown to be sensitive to the transition to the incommensurate regime. We then focus on the behavior of the zero-field susceptibility through an effective Curie constant. At zero-temperature, we give doping-dependent corrections to the results of Sigrist and Furusaki on general bipartite lattices, and compute exactly the distribution of ladder clusters due to chain breaking effects. Solving the effective model with exact diagonalization and quantum Monte-Carlo gives the temperature dependence of the Curie constant. Its high-temperature limit is understood within a random dimer model, while the low-temperature tail is compatible with a real-space renormalization group scenario. Interestingly, solving the full microscopic model does not show a plateau corresponding to the saturation of the impurities in isotropic ladders. The second magnetic response which is analyzed is the magnetic curve. Below fields of the order of the spin gap, the magnetization process is controlled by the physics of interacting impurity spins. The random dimer model is shown to capture the bulk of the curve, accounting for the deviation from a Brillouin behavior due to interactions. The effective model calculations agree rather well with density-matrix renormalization group calculations at zero temperature, and with quantum Monte-Carlo at finite temperature. In all, the effect of incommensurability does not display a strong qualitative effect on both the magnetic susceptibility and the magnetic curve. Consequences for experiments on the BiCu2PO6 compound and other spin-gapped materials are briefly mentioned.
We study the effect of disorder on frustrated dimerized spin-1/2 chains at the Majumdar-Ghosh point. Using variational methods and density-matrix renormalization group approaches, we identify two localization mechanisms for spinons which are the deconfined fractional elementary excitations of these chains. The first one belongs to the Anderson localization class and dominates at the random Majumdar-Ghosh (RMG) point. There, spinons are almost independent, remain gapped, and localize in Lifshitz states whose localization length is analytically obtained. The RMG point then displays a quantum phase transition to phase of localized spinons at large disorder. The other mechanism is a random confinement mechanism which induces an effective interaction between spinons and brings the chain into a gapless and partially polarized phase for arbitrarily small disorder.PACS numbers: 75.10. Kt, 75.40.Mg, 75.10.Jm, 75.10.Pq Spinons are fractional excitations corresponding to half of a spin excitation in quantum magnets. They typically appear in understanding the excitation spectrum of one-dimensional systems such as the frustrated J 1 − J 2 Heisenberg chain. This model possesses an exact ground-state at the MajumdarGhosh (MG) point J 1 = 2J 2 [1] which is the prototype of a valence bond solid (VBS) state and for which a variational approach describes well elementary excitations [2]. Further, spinons play a crucial role in unconventional two-dimensional phase transitions in which they could be deconfined [3]. Investigating the effect of disorder on their dynamics is all the more essential, since randomness is inherent to experimental samples. Possible strategies to study random quantum magnets are bosonization [4], provided the disorder is small, or realspace renormalization group (RSRG) [5], rather suited for the strong disorder regime. The latter is asymptotically exact in the case of an infinite-disorder fixed point [6], but when it converges to a finite-disorder fixed point, its outcome can be questioned at small disorder. Numerical approaches are challenging due to strong finite-size effects from rare events [7] and the interplay between frustration and disorder cannot be addressed using the powerful quantum Monte-Carlo method because of the sign problem. Lastly, most studies on random magnets focus on the ground-state while little is known about the fate of elementary excitations. So far, it has been conjectured [8] that the gap of frustrated dimerized chains is broken by a domain formation mechanism similar to the one suggested for Mott phases [9]. Later, RSRG studies [10] found that it would belong to the class of the large-spin phase [11].In this Letter, two localization mechanisms at play in random frustrated dimerized chains are unveiled using a variational approach supported by density-matrix renormalization group (DMRG) calculations [12]. They provide both quantitative predictions and an intuitive picture of the physics. The first mechanism belongs to the Anderson class and governs the dynamics of a spinon at th...
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