Response of finite spin-S Heisenberg chains to local perturbations

We consider the properties of finite isotropic antiferromagnetic Heisenberg chains with S=1/2, 1, 3/2 spins when a weak magnetic field is applied on a few sites, using White's density matrix renormalization group (DMRG) method. For the S=1 chain there exists only one length scale in the system which determines the behavior of the one- and two-point correlation functions both around the local perturbation and near the free boundary. For the critical, half-odd-integer spin cases the exponent of the spin-spin correlation function was found to be $\eta=1$, and the exponent of the decay of the site magnetization around the perturbed site is $x_m =\eta /2$. Close to a free boundary, however, the behavior is completely different for S=1/2 and $S > 1/2$.Comment: 13 pages, 7 figure

Spin-orbit coupling and electron spin resonance for interacting electrons in carbon nanotubes

We review the theoretical description of spin-orbit scattering and electron spin resonance in carbon nanotubes. Particular emphasis is laid on the effects of electron-electron interactions. The spin-orbit coupling is derived, and the resulting ESR spectrum is analyzed both using the effective low-energy field theory and numerical studies of finite-size Hubbard chains and two-leg Hubbard ladders. For single-wall tubes, the field theoretical description predicts a double peak spectrum linked to the existence of spin-charge separation. The numerical analysis basically confirms this picture, but also predicts additional features in finite-size samples.Comment: 19 pages, 4 figures, invited review article for special issue in J. Phys. Cond. Mat., published versio

Density matrix renormalisation group for a quantum spin chain at non-zero temperature

We apply a recent adaptation of White's density matrix renormalisation group (DMRG) method to a simple quantum spin model, the dimerised $XY$ chain, in order to assess the applicabilty of the DMRG to quantum systems at non-zero temperature. We find that very reasonable results can be obtained for the thermodynamic functions down to low temperatures using a very small basis set. Low temperature results are found to be most accurate in the case when there is a substantial energy gap.Comment: 6 pages, Standard Latex File + 7 PostScript figures available on reques

The Density Matrix Renormalization Group applied to single-particle Quantum Mechanics

A simplified version of White's Density Matrix Renormalization Group (DMRG) algorithm has been used to find the ground state of the free particle on a tight-binding lattice. We generalize this algorithm to treat the tight-binding particle in an arbitrary potential and to find excited states. We thereby solve a discretized version of the single-particle Schr\"odinger equation, which we can then take to the continuum limit. This allows us to obtain very accurate results for the lowest energy levels of the quantum harmonic oscillator, anharmonic oscillator and double-well potential. We compare the DMRG results thus obtained with those achieved by other methods.Comment: REVTEX file, 21 pages, 3 Tables, 4 eps Figure

A Renormalization Group Method for Quasi One-dimensional Quantum Hamiltonians

A density-matrix renormalization group (DMRG) method for highly anisotropic two-dimensional systems is presented. The method consists in applying the usual DMRG in two steps. In the first step, a pure one dimensional calculation along the longitudinal direction is made in order to generate a low energy Hamiltonian. In the second step, the anisotropic 2D lattice is obtained by coupling in the transverse direction the 1D Hamiltonians. The method is applied to the anisotropic quantum spin half Heisenberg model on a square lattice.Comment: 4 pages, 4 figure

An Improved Initialization Procedure for the Density-Matrix Renormalization Group

We propose an initialization procedure for the density-matrix renormalization group (DMRG): {\it the recursive sweep method}. In a conventional DMRG calculation, the infinite-algorithm, where two new sites are added to the system at each step, has been used to reach the target system size. We then need to obtain the ground state for a different system size for every site addition, so 1) it is difficult to supply a good initial vector for the numerical diagonalization for the ground state, and 2) when the system reduced to a 1D system consists of an array of nonequivalent sites as in ladders or Hubbard-Holstein model, special care has to be taken. Our procedure, which we call the {\it recursive sweep method}, provides a solution to these problems and in fact provides a faster algorithm for the Hubbard model as well as more complicated ones such as the Hubbard-Holstein model.Comment: 4 pages, 4 figures, submitted to JPS

Two-state behaviour of Kondo trimers

The electronic properties and spectroscopic features of a magnetic trimer with a Kondo-like coupling to a non-magnetic metallic substrate are analyzed at zero temperature. The substrate density of states is depressed in the trimer neighbourhood, being exactly zero at the substrate chemical potential. The size of the resonance strongly depends on the magnetic state of the trimer, and exhibits a two-state behavior. The geometrical dependence of these results agree qualitatively with recent experiments and could be reproduced in a triangular quantum dot arrangement.Comment: 5 pages, including 4 figure

Correlation amplitude for S=1/2 XXZ spin chain in the critical region

The density-matrix renormalization-group technique is used to calculate the spin correlation functions and of the one-dimensional S=1/2 XXZ model in the gapless regime. The numerical results for open chains of 200 spins are analyzed by comparing them with correlation functions calculated from a low-energy field theory. This gives precise estimates of the amplitudes of the correlation functions in the thermodynamic limit. The exact amplitude recently conjectured by Lukyanov and Zamolodchikov and the logarithmic correction in the Heisenberg model are confirmed numerically.Comment: 4 pages, 3 figures, final versio

Dynamical Correlation Functions using the Density Matrix Renormalization Group

The density matrix renormalization group (DMRG) method allows for very precise calculations of ground state properties in low-dimensional strongly correlated systems. We investigate two methods to expand the DMRG to calculations of dynamical properties. In the Lanczos vector method the DMRG basis is optimized to represent Lanczos vectors, which are then used to calculate the spectra. This method is fast and relatively easy to implement, but the accuracy at higher frequencies is limited. Alternatively, one can optimize the basis to represent a correction vector for a particular frequency. The correction vectors can be used to calculate the dynamical correlation functions at these frequencies with high accuracy. By separately calculating correction vectors at different frequencies, the dynamical correlation functions can be interpolated and pieced together from these results. For systems with open boundaries we discuss how to construct operators for specific wavevectors using filter functions.Comment: minor revision, 10 pages, 15 figure

Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal Operators

Field theory calculations predict multiplicative logarithmic corrections to correlation functions from marginally irrelevant operators. However, for the numerically most suitable model - the spin-1/2 chain - these corrections have been controversial. In this paper, the spin-spin correlation function of the antiferromagnetic spin-1/2 chain is calculated numerically in the presence of a next nearest neighbor coupling J2 for chains of up to 32 sites. By varying the coupling strength J2 we can control the effect of the marginal operator, and our results unambiguously confirm the field theory predictions. The critical value at which the marginal operator vanishes has been determined to be at J2 = 0.241167 +/- 0.000005J.Comment: revised paper with extended data-analysis. 5 pages, using revtex with 4 embedded figures (included with macro). A complete postscript file with all figures + text (5 pages) is available from http://FY.CHALMERS.SE/~eggert/marginal.ps or by request from [email protected]