The projector Monte Carlo method and finite-size scaling are applied to the solution of the ground-state properties of the ``Kondo necklace'' Hamiltonian. The energy and various spin-spin correlation functions are calculated for chains up to 16 sites in length. Correlations between the spins on different sites are evaluated, and the nature of the ground-state phase as a function of the ratio of the exchange coupling J to the bandwidth W is examined. Evaluation of the correlation function 〈S\ensuremath{\rightarrow}(i)\ensuremath{\cdot}\ensuremath{\tau}\ensuremath{\rightarrow}(i)〉 shows that as the coupling between the localized S spins and the \ensuremath{\tau} spin chain increases, the system becomes composed of independent singlets on each site. Contrary to both mean-field and various approximate renormalization-group calculations, we find that our results are consistent with an absence of magnetic order as soon as J is different from 0.
The projector Monte Carlo method and finite-size scaling are applied to the solution of the ground-state properties of the ``Kondo necklace'' Hamiltonian. The energy and various spin-spin correlation functions are calculated for chains up to 16 sites in length. Correlations between the spins on different sites are evaluated, and the nature of the ground-state phase as a function of the ratio of the exchange coupling J to the bandwidth W is examined. Evaluation of the correlation function 〈S\ensuremath{\rightarrow}(i)\ensuremath{\cdot}\ensuremath{\tau}\ensuremath{\rightarrow}(i)〉 shows that as the coupling between the localized S spins and the \ensuremath{\tau} spin chain increases, the system becomes composed of independent singlets on each site. Contrary to both mean-field and various approximate renormalization-group calculations, we find that our results are consistent with an absence of magnetic order as soon as J is different from 0.
A recently proposed density-matrix renormalization group is used to investigate the ground-state properties of the Kondo-necklace Hamiltonian. It represents a chain of XY interacting pseudospins that are Kondo coupled (J) to localized spins. The spin gap as well as the short- and long-range spin correlation functions are consistent with the existence of a smooth crossover at J\ensuremath{\approxeq}0.5. For J\ensuremath{\le}0.5, the gap depends exponentially on ${\mathit{J}}^{\mathrm{\ensuremath{-}}1/2}$ and the in-plane correlation function of the localized spins shows RKKY oscillations while the z one falls monotonically in contrast to the XY behavior. The correlation length diverges at J=0. For J\ensuremath{\ge}0.5, the gap is linearly increasing with J, and the system is made of nearly independent singlets.
Ground-state properties of the one-dimensional Kondo lattice model are investigated using the quantum Monte Carlo (QMC) simulation method. To reduce the difficulty of the negative sign problem, we employ the variationally optimized singlet wave function. Since the improvement of Monte Carlo sampling efficiency is achieved in the half-filling case, we can perform the simulations on large systems (up to 26-site system). The QMC data on the local spin correlations are closely compared with those of the variational Monte Carlo (VMC) calculations as well as with the exact diagonalization data of the Ruderman-Kittel-Kasuya-Yoshida (RKKY) lattice model. We find that the local spin correlation decays exponentially with the correlation length ${\ensuremath{\xi}}_{\mathit{f}\mathit{f}}$\ensuremath{\sim}2.54 in the QMC data, while ${\ensuremath{\xi}}_{\mathit{f}\mathit{f}}$\ensuremath{\sim}1.08 in the VMC results (J/t=1). This implies the absence of the long-range order (the existence of the spin gap) and the importance of intersite correlation effects which are not taken into account in the VMC results. On the other hand, the system size dependence is almost absent in the Kondo lattice model results, which contrasts the behavior in the RKKY data.
We study the low-energy sector of the Heisenberg necklace model. Using the field-theory methods, we estimate how the coupling of the electronic spins with the paramagnetic Kondo spins affects the overall spin dynamics and evaluate its dependence on a magnetic field. We are motivated by the experimental realizations of the spin-1/2 Heisenberg chains in SrCuO2 and Sr2CuO3 cuprates, which remain one-dimensional Luttinger liquids down to temperatures much lower than the in-chain exchange coupling J. We consider the perturbation of the energy spectrum caused by the interaction $\ensuremath{\gamma}$ with nuclear spins (I=3/2) present on the same sites. We find that the resulting necklace model has a characteristic energy scale, $\mathrm{\ensuremath{\Lambda}}\ensuremath{\sim}{J}^{1/3}{(\ensuremath{\gamma}I)}^{2/3}$, at which the coupling between (nuclear) spins of the necklace and the spins of the Heisenberg chain becomes strong. This energy scale is insensitive to a magnetic field B. For ${\ensuremath{\mu}}_{B}B>\mathrm{\ensuremath{\Lambda}}$ we find two gapless bosonic modes that have different velocities, whose ratio at strong fields approaches a universal number, 2+1.
The Kondo effect in a one-dimensional spin-21XXZ model in the gapless XY regime $(\ensuremath{-}1<\ensuremath{\Delta}<~1)$ is studied both analytically and numerically. In our model an impurity spin (S=1/2) is coupled to a single spin in the XXZ spin chain. Perturbative renormalization-group (RG) analysis is performed for various limiting cases to deduce low-energy fixed points. It is shown that in the ground state the impurity spin is screened by forming a singlet with a spin in the host XXZ chain. In the antiferromagnetic side $(0<\ensuremath{\Delta}<~1)$ the host chain is cut into two semi-infinite chains by the singlet. In the ferromagnetic side $(\ensuremath{-}1<\ensuremath{\Delta}<0),$ on the other hand, the host XXZ chain remains as a single chain through ``healing'' of a weakened bond in the low-energy (long-distance) limit. The density-matrix renormalization-group method is used to study the size scaling of finite-size energy gaps and the power-law decay of correlation functions in the ground state. The numerical results are in good agreement with the predictions of the RG analysis. Low-temperature behaviors of specific heat and susceptibility are also discussed.
The density matrix renormalization group and quantum Monte Carlo methods are used to describe coupled trimer chains in a magnetic field h. The Hamiltonian contains exchange terms involving the intratrimer coupling J1 (taken as the unit of energy) and the intertrimer coupling J2, plus the Zeeman interaction for a magnetic field h along the z direction. Results for the magnetization per trimer m are calculated in regimes of positive and negative values of the ratio J=J2/J1, from which the rich field-induced ground state phase diagram h versus J is derived, with the presence of a Luttinger liquid, the 1/3 plateau (m=1/2), and the one of fully polarized magnetization (m=3/2). Also, zero-field Lanczos calculation of the spin-wave dispersion from the 1/3 plateau for Sz=1 is shown at the previous regimes of J values. In addition, we also report on the decay of correlation functions of trimers along open chains, as well as the average two-magnon distribution. The ground state is ferrimagnetic for $0<J\ensuremath{\le}1$, and is a singlet for $\ensuremath{-}1\ensuremath{\le}J<0$. In the singlet phase, the spin correlation functions along the legs present an antiferromagnetic power-law decay, similar to the spin-1/2 linear chain, thus suggesting that the ground state is made of three coupled antiferromagnetically oriented chains. In the singlet phase, the dimensionless thermal magnetic susceptibility per site normalized by 1/∣J∣ gets closer to $1/{\ensuremath{\pi}}^{2}$ as the temperature $T\ensuremath{\rightarrow}0$. For the ferrimagnetic phase, we fit the susceptibility to the experimental data for the compound Pb3Cu3(PO4)4 and estimate the model exchange couplings: J1=74.8K and J=0.4. These values imply a range of energies for the magnon excitations that are in accord with the data from neutron scattering experiments on Pb3Cu3(PO4)4 for two excitation modes. The 1/3 plateau closes only at 1/∣J∣=0 with J<0.
Abstract Using the density matrix renormalization group method, we study the one‐dimensional Kondo necklace model including two anisotropies: η in the XY interaction of the conduction chain, and Δ in the local Kondo coupling between localized and conduction spins. For different values of the anisotropies, we calculate the energy gap and estimate the quantum critical points in which a phase transition from antiferromagnetic to spin liquid states takes place, assuming a Kosterlitz–Thouless‐like behavior. For the case η=0 , the system remains in a spin liquid state for the different Δ considered, but when η=0 , Δ markedly affects the location of the critical points. We also calculate correlation functions for a specific case, in order to support our gap results.