Overscreened Single Channel Kondo Problem

We consider the single channel Kondo problem with the Kondo coupling between a spin $S$ impurity and conduction electrons with spin $j$. These problems arise as multicritical points in the parameter spaces of two- and higher-level tunneling systems, and some impurity models of heavy fermion compounds. In contrast to the previous Bethe-anstaz conjectures, it turns out that the dynamics of the spin sector is the same as that of a spin $S$ impurity coupled to $k(j)$ channels of spin $1/2$ electrons with $k(j) = 2j(j+1)(2j+1)/3$. As a result, for $2S < k(j)$, the system shows non-Fermi liquid behavior with the same exponents for the thermodynamic quantities as those of $k(j)$ channel Kondo problem. However, both the finite-size spectrum and the operator content are different due to the presence of the other sectors and can be obtained by conformal field theory techniques.Comment: 4 pages, revtex, no figures. Revised Versio

Charge dynamics in half-filled Hubbard chains with finite on-site interaction

We study the charge dynamic structure factor of the one-dimensional Hubbard model with finite on-site repulsion U at half filling. Numerical results from the time-dependent density matrix renormalization group are analyzed by comparison with the exact spectrum of the model. The evolution of the line shape as a function of U is explained in terms of a relative transfer of spectral weight between the two-holon continuum that dominates in the limit U\to \infty and a subset of the two-holon-two-spinon continuum that reconstructs the electron-hole continuum in the limit U\to 0. Power-law singularities along boundary lines of the spectrum are described by effective impurity models that are explicitly invariant under spin and \eta-spin SU(2) rotations. The Mott-Hubbard metal-insulator transition is reflected in a discontinuous change of the exponents of edge singularities at U=0. The sharp feature observed in the spectrum for momenta near the zone boundary is attributed to a Van Hove singularity that persists as a consequence of integrability.Comment: 22 pages, 13 figure

Decoupling of the S=1/2 antiferromagnetic zig-zag ladder with anisotropy

The spin-1/2 antiferromagnetic zig-zag ladder is studied by exact diagonalization of small systems in the regime of weak inter-chain coupling. A gapless phase with quasi long-range spiral correlations has been predicted to occur in this regime if easy-plane (XY) anisotropy is present. We find in general that the finite zig-zag ladder shows three phases: a gapless collinear phase, a dimer phase and a spiral phase. We study the level crossings of the spectrum,the dimer correlation function, the structure factor and the spin stiffness within these phases, as well as at the transition points. As the inter-chain coupling decreases we observe a transition in the anisotropic XY case from a phase with a gap to a gapless phase that is best described by two decoupled antiferromagnetic chains. The isotropic and the anisotropic XY cases are found to be qualitatively the same, however, in the regime of weak inter-chain coupling for the small systems studied here. We attribute this to a finite-size effect in the isotropic zig-zag case that results from exponentially diverging antiferromagnetic correlations in the weak-coupling limit.Comment: to appear in Physical Review

Non-Fermi Liquid Behavior in Dilute Quadrupolar System Prx_{x}La1−x_{1-x}Pb3_3 with xx≤\le0.05

We have studied the low-temperature properties of Pr$_{x}$La$_{1-x}$Pb$_{3}$ with non-Kramers $\Gamma_{3}$ quadrupolar moments of the crystal-electric-field ground state, for a wide concentration range of Pr ions. For $x$$\le$0.05, the specific heat $C/T$ increases monotonically below $T$=1.5 K, which can be scaled with a characteristic temperature $T^{*}$ defined at each concentration $x$. The electrical resistivity $\rho$$(T)$ in the corresponding temperature region shows a marked decrease deviating from a Fermi-liquid behavior $\rho$$(T)$$\propto$$T^{2}$. The Kondo effect arising from the correlation between the dilute $\Gamma_{3}$ moments and the conduction electrons may give rise to such anomalous behavior

Interplay of disorder and magnetic field in the superconducting vortex state

We calculate the density of states of an inhomogeneous superconductor in a magnetic field where the positions of vortices are distributed completely at random. We consider both the cases of s-wave and d-wave pairing. For both pairing symmetries either the presence of disorder or increasing the density of vortices enhances the low energy density of states. In the s-wave case the gap is filled and the density of states is a power law at low energies. In the d-wave case the density of states is finite at zero energy and it rises linearly at very low energies in the Dirac isotropic case (\alpha_D=t/\Delta_0=1, where t is the hopping integral and \Delta_0 is the amplitude of the order parameter). For slightly higher energies the density of states crosses over to a quadratic behavior. As the Dirac anisotropy increases (as \Delta_0 decreases with respect to the hopping term) the linear region decreases in width. Neglecting this small region the density of states interpolates between quadratic and back to linear as \alpha_D increases. The low energy states are strongly peaked near the vortex cores.Comment: 12 REVTeX pages, 15 figure

Spin dynamics of the S=1/2 antiferromagnetic zig-zag ladder with anisotropy

We use exact diagonalization and the modified Lanczos method to study the finite energy and finite momentum spectral weight of the longitudinal and transverse spin excitations of the anisotropic zig-zag ladder. We find that the spin excitations form continua of gapless or gapped spinons in the different regions of the phase diagram. The results obtained are consistent with a picture previously proposed that in the anisotropic case there is a transition from a gapped regime to a gapless regime, for small interchain coupling. In this regime we find a sharp low-energy peak in the structure function for the transverse spin excitations, consistent with a finite stiffness.Comment: 17 figure

On the ground-state properties of antiferromagnetic half-integer spin chains with long-range interactions

The Lieb-Shultz-Mattis theorem is extended to Heisenberg chains with long-range interactions. We prove that the half-integer spin chain has no gap, if it possesses unique ground state and the exchange decays faster than the inverse-square of distance between spins. The results can be extended to a wide class of one-dimensional models.Comment: 3 pages, RevTeX

Thermodynamics of the bilinear-biquadratic spin one Heisenberg chain

The magnetic susceptibility and specific heat of the one-dimensional S=1 bilinear-biquadratic Heisenberg model are calculated using the transfer matrix renormalization group. By comparing the results with the experimental data of ${\rm LiVGe_2O_6}$ measured by Millet et al. (Phys. Rev. Lett. {\bf 83}, 4176 (1999)), we find that the susceptibility data of this material, after subtracting the impurity contribution, can be quantitatively explained with this model. The biquadratic exchange interaction in this material is found to be ferromagnetic, i.e. with a positive coupling constant.Comment: 4 pages, 4 postscript figure

Simple Bosonization Solution of the 2-channel Kondo Model: I. Analytical Calculation of Finite-Size Crossover Spectrum

We present in detail a simple, exact solution of the anisotropic 2-channel Kondo (2CK) model at its Toulouse point. We reduce the model to a quadratic resonant-level model by generalizing the bosonization-refermionization approach of Emery and Kivelson to finite system size, but improve their method in two ways: firstly, we construct all boson fields and Klein factors explicitly in terms of the model's original fermion operators $c_{k \sigma j}$, and secondly we clarify explicitly how the Klein factors needed when refermionizing act on the original Fock space. This enables us to explicitly follow the adiabatic evolution of the 2CK model's free-fermion states to its exact eigenstates, found by simply diagonalizing the resonant-level model for arbitrary magnetic fields and spin-flip coupling strengths. In this way we obtain an {\em analytic} description of the cross-over from the free to the non-Fermi-liquid fixed point. At the latter, it is remarkably simple to recover the conformal field theory results for the finite-size spectrum (implying a direct proof of Affleck and Ludwig's fusion hypothesis). By analyzing the finite-size spectrum, we directly obtain the operator content of the 2CK fixed point and the dimension of various relevant and irrelevant perturbations. Our method can easily be generalized to include various symmetry-breaking perturbations. Furthermore it establishes instructive connections between different renormalization group schemes such as poor man's scaling, Anderson-Yuval type scaling, the numerical renormalization group and finite-size scaling.Comment: 35 pages Revtex, 7 figures, submitted to Phys. Rev.

Anderson-Yuval approach to the multichannel Kondo problem

We analyze the structure of the perturbation expansion of the general multichannel Kondo model with channel anisotropic exchange couplings and in the presence of an external magnetic field, generalizing to this case the Anderson-Yuval technique. For two channels, we are able to map the Kondo model onto a generalized resonant level model. Limiting cases in which the equivalent resonant level model is solvable are identified. The solution correctly captures the properties of the two channel Kondo model, and also allows an analytic description of the cross-over from the non Fermi liquid to the Fermi liquid behavior caused by the channel anisotropy.Comment: 23 pages, ReVTeX, 4 figures av. on reques