We theoretically study a spin-spin correlation enhanced by non-magnetic impurities in a frustrated two-leg spin ladder. The frustration is introduced by the next-nearest-neighbor antiferromagnetic interaction in the leg direction in the antiferromagnetic two-leg spin ladder. The spin-spin correlation function around impurity site is calculated by the density-matrix renormalization-group method. We find that the spin-spin correlation is enhanced around impurity site with the wavenumber reflecting the frustration. As increasing the frustration, the wavenumber is shifted from commensurate to incommensurate. We discuss several experimental results on BiCu2PO6 in the light of our theory.
We theoretically study the magnetic excitations in a frustrated two-leg spin-ladder system, in which antiferromagnetic exchange interactions act on the nearest-neighbor and next-nearest-neighbor bonds in the leg direction, and on the nearest-neighbor bonds in the rung direction. A dynamical spin correlation function at zero temperature is calculated using the dynamical density-matrix renormalization-group method for possible magnetic phases, i.e., columnar-dimer and rung-singlet phases. The columnar-dimer phase is characterized by multispinon excitations with a spin gap, whereas the rung-singlet phase is dominated by the triplet excitation in the rung direction. One major difference found between these two phases appears in the spectral weight of magnetic excitations, in particular, the bonding and antibonding modes in the rung direction. Therefore, we can distinguish one phase from the other by the difference in the spectral weight. Furthermore, we examine the effect of frustration on both modes in the rung-singlet phase with a perturbation theory from the strong coupling limit. The antibonding mode is shown to be stable against frustration, and a wave number with minimum excitation energy is shifted from being commensurate to being incommensurate. In contrast, the bonding mode is merged into the continuum excitation of multiple triplet excitations by increasing frustration. By comparing our results with inelastic neutron scattering experiments for BiCu
2PO
6, the magnitude of the magnetic exchange interactions and the ground state will be determined.
Using the density matrix renormalization group technique, we investigate the quantum phase diagram of a ferromagnetic frustrated two-leg spin-1/2 ladder with diagonal and in-chain next-nearest-neighbor (NNN) interactions. By analyzing the correlation function and four-site entropy, we obtain the quantum phase diagram of the system. We find that the system possesses a tetramer phase, a ferromagnetic phase and states I and II. Spin arrangements for states I and II are also determined. In addition, the influence of the in-chain NNN interaction J 2 on the phase transitions of the anti-ferromagnetic case is studied. We show the phase diagram and find that the stagger dimer phase exists only in a narrow parameter region. Meanwhile, the existence of the controversial columnar dimer phase at J 2 = 0 is carefully analyzed.
We derive and investigate the microscopic model of the quantum magnet
BiCu2PO6 using band-structure calculations, magnetic susceptibility and high-field magnetization measurements, as well as exact diagonalization (ED) and density-matrix renormalization group (DMRG) techniques. The resulting quasi-one-dimensional spin model is a two-leg antiferromagnetic ladder with frustrating next-nearest-neighbor couplings along the legs. The individual couplings are estimated from band-structure calculations and by fitting the magnetic susceptibility with theoretical predictions, obtained using full diagonalizations. The nearest-neighbor leg coupling
J1, the rung coupling
J4, and one of the next-nearest-neighbor couplings
J2 amount to 120--150 K while the second next-nearest-neighbor coupling is ${J}_{2}^{\ensuremath{'}}\ensuremath{\simeq}{J}_{2}/2$. The spin ladders do not match the structural chains, and although the next-nearest-neighbor interactions
J2 and ${J}_{2}^{\ensuremath{'}}$ have very similar superexchange pathways, they differ substantially in magnitude due to a tiny difference in the O-O distances and in the arrangement of nonmagnetic
PO4 tetrahedra. An extensive ED study of the proposed model provides the low-energy excitation spectrum and shows that the system is in the strong rung coupling regime. The strong frustration by the next-nearest-neighbor couplings leads to a triplon branch with an incommensurate minimum. This is further corroborated by a strong-coupling expansion up to second order in the inter-rung coupling. Based on high-field magnetization measurements, we estimate the spin gap of $\ensuremath{\Delta}\ensuremath{\simeq}32\text{ }\text{K}$ and suggest the likely presence of antisymmetric Dzyaloshinskii-Moriya anisotropy and interladder coupling
J3. We also provide a tentative description of the physics of
BiCu2PO6 in magnetic field, in the light of the low-energy excitation spectra and numerical calculations based on ED and DMRG. In particular, we raise the possibility for a rich interplay between one- and two-component Luttinger liquid phases and a magnetization plateau at 1/2 of the saturation value.
The interplay between the Kondo effect, indirect magnetic interaction, and geometrical frustration is studied in the Kondo lattice on the one-dimensional zigzag ladder. Using the density-matrix renormalization group, the ground-state and various short- and long-range spin- and density-correlation functions are calculated for the model at half filling as a function of the antiferromagnetic Kondo interaction down to
J=0.3t, where
t is the nearest-neighbor hopping on the zigzag ladder. Geometrical frustration is shown to lead to at least two critical points: Starting from the strong-
J limit, where almost local Kondo screening dominates and where the system is a nonmagnetic Kondo insulator, antiferromagnetic correlations between nearest-neighbor and next-nearest-neighbor local spins become stronger and stronger, until at ${J}_{\mathrm{c}}^{\mathrm{dim}}\ensuremath{\approx}0.89t$ frustration is alleviated by a spontaneous breaking of translational symmetry and a corresponding transition to a dimerized state. This is characterized by antiferromagnetic correlations along the legs and by alternating antiferro- and ferromagnetic correlations on the rungs of the ladder. A mechanism of partial Kondo screening that has been suggested for the Kondo lattice on the two-dimensional triangular lattice is not realized in the one-dimensional case. Furthermore, within the symmetry-broken dimerized state, there is a magnetic transition to a ${90}^{\ensuremath{\circ}}$ quantum spin spiral with quasi-long-range order at ${J}_{\mathrm{c}}^{\mathrm{mag}}\ensuremath{\approx}0.84t$. The quantum-critical point is characterized by a closure of the spin gap (with decreasing
J) and a divergence of the spin-correlation length and of the spin-structure factor
S(q) at wave vector $q=\ensuremath{\pi}/2$. This is opposed to the model on the one-dimensional bipartite chain, which is known to have a finite spin gap for all
J>0 at half filling.
Magnetic correlations are studied in a two-leg Hubbard ladder doped with nonmagnetic impurities using finite temperature quantum Monte Carlo (FTQMC) method. A number of relevant macroscopic quantities calculated as a function of temperature T and impurity concentration are found to exhibit significantly renormalized behavior, a feature noted in many experiments. The uniform magnetic susceptibility χ0(T) for the impurity doped system shows a cusplike behavior followed by a sharp increase at lower temperatures, signaling the formation of impurity induced free magnetic moments, while it diminishes rapidly for the pure system. The spin correlations are found to increase in the vicinity of an impurity. To investigate the effect of nonmagnetic impurities on the spin wave modes in the system, spin wave velocity vsw is calculated as a function of impurity concentration. The result shows that vsw is reduced by nonmagnetic impurities, indicating softening of the modes. Simulations are performed slightly away from half filling and kinetic energy of the electrons in the neighborhood of an impurity site is calculated to study the interplay between impurities and holes. However, contrary to previous experimental observations on two dimensional lattices where nonmagnetic impurities reduce hole mobility, no noticeable effect of impurity on the mobility of the neighboring electrons is found in our calculation.