An introduction to numerical methods in low-dimensional quantum systems

This is an introductory course to the Lanczos Method and Density Matrix Renormalization Group Algorithms(DMRG), two among the leading numerical techniques applied in studies of low-dimensional quantum models. The idea of studying the models on clusters of a finite size in order to extract their physical properties is briefly discussed. The important role played by the model symmetries is also examined. Special emphasis is given to the DMRG.Comment: 36 pages, 4 figures, standard LaTex, Brazilian School on Statistical Mechanics (2002), PDF and PS files available at http://www.sbf.if.usp.br/bj

Absence of a true long-range orbital order in a two-leg Kondo ladder

We investigate, through the density-matrix renormalization group and the Lanczos technique, the possibility of a two-leg Kondo ladder present an incommensurate orbital order. Our results indicate a staggered short-range orbital order at half-filling. Away from half-filling our data are consistent with an incommensurate quasi-long-range orbital order. We also observed that an interaction between the localized spins enhances the rung-rung current correlations.Comment: 7 pages, 6 figures, changed the introduction and added some discussion

Effects of nanoscale spatial inhomogeneity in strongly correlated systems

We calculate ground-state energies and density distributions of Hubbard superlattices characterized by periodic modulations of the on-site interaction and the on-site potential. Both density-matrix renormalization group and density-functional methods are employed and compared. We find that small variations in the on-site potential $v_i$ can simulate, cancel, or even overcompensate effects due to much larger variations in the on-site interaction $U_i$. Our findings highlight the importance of nanoscale spatial inhomogeneity in strongly correlated systems, and call for reexamination of model calculations assuming spatial homogeneity.Comment: 5 pages, 1 table, 4 figures, to appear in PR

Modulation of charge-density waves by superlattice structures

We discuss the interplay between electronic correlations and an underlying superlattice structure in determining the period of charge density waves (CDW's), by considering a one-dimensional Hubbard model with a repeated (non-random) pattern of repulsive (U>0) and free (U=0) sites. Density matrix renormalization group diagonalization of finite systems (up to 120 sites) is used to calculate the charge-density correlation function and structure factor in the ground state. The modulation period can still be predicted through effective Fermi wavevectors, k_F*, and densities, and we have found that it is much more sensitive to electron (or hole) doping, both because of the narrow range of densities needed to go from q*=0 to \pi, but also due to sharp 2k_F*-4k_F* transitions; these features render CDW's more versatile for actual applications in heterostructures than in homogeneous systems.Comment: 4 pages, 5 figures, to appear in Phys Rev

Quantum Correlations and Coherence in Spin-1 Heisenberg Chains

We explore quantum and classical correlations along with coherence in the ground states of spin-1 Heisenberg chains, namely the one-dimensional XXZ model and the one-dimensional bilinear biquadratic model, with the techniques of density matrix renormalization group theory. Exploiting the tools of quantum information theory, that is, by studying quantum discord, quantum mutual information and three recently introduced coherence measures in the reduced density matrix of two nearest neighbor spins in the bulk, we investigate the quantum phase transitions and special symmetry points in these models. We point out the relative strengths and weaknesses of correlation and coherence measures as figures of merit to witness the quantum phase transitions and symmetry points in the considered spin-1 Heisenberg chains. In particular, we demonstrate that as none of the studied measures can detect the infinite order Kosterlitz-Thouless transition in the XXZ model, they appear to be able to signal the existence of the same type of transition in the biliear biquadratic model. However, we argue that what is actually detected by the measures here is the SU(3) symmetry point of the model rather than the infinite order quantum phase transition. Moreover, we show in the XXZ model that examining even single site coherence can be sufficient to spotlight the second-order phase transition and the SU(2) symmetry point.Comment: 8 pages. 5 figure

Bethe Ansatz solutions for Temperley-Lieb Quantum Spin Chains

We solve the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups ${\cal U}_{q}(X_{n})$ for $X_{n}=A_{1},$ $B_{n},$ $C_{n}$ and $D_{n}$. The tool is a modified version of the coordinate Bethe Ansatz through a suitable choice of the Bethe states which give to all models the same status relative to their diagonalization. All these models have equivalent spectra up to degeneracies and the spectra of the lower dimensional representations are contained in the higher-dimensional ones. Periodic boundary conditions, free boundary conditions and closed non-local boundary conditions are considered. Periodic boundary conditions, unlike free boundary conditions, break quantum group invariance. For closed non-local cases the models are quantum group invariant as well as periodic in a certain sense.Comment: 28 pages, plain LaTex, no figures, to appear in Int. J. Mod. Phys.

Seasonal effect on the technological and chemical traits of sheep "ricotta Pistoiese" cheese

The "ricotta di pecora pistoiese" is comprised in the list of the traditional agrofood products of Tuscany and the relative PDO (Protected Designation of Origin) has be required. This research, analysing the making process, aimed to evaluate its chemical and nutritive traits as influenced by some factors, with particular attention to the season. During the four seasons of two consecutive years, the making process of ricotta cheese was monitored in four farms for a total of 32 control-days. Yields, chemical composition and fatty acid profile of fat were determined. The amount of milk added to whey influenced the fat and protein content and the yields at 0 and 24 hours. Season affected only the protein content, higher in winter and spring. Fatty acid composition was influenced strongly by the season being the ricotta cheese of summer richer of monounsaturated and polyunsaturated FA than that of autumn and winter, probably due to the feeding regimen based mainly on fresh grass

Magnetic Susceptibility of an integrable anisotropic spin ladder system

We investigate the thermodynamics of a spin ladder model which possesses a free parameter besides the rung and leg couplings. The model is exactly solved by the Bethe Ansatz and exhibits a phase transition between a gapped and a gapless spin excitation spectrum. The magnetic susceptibility is obtained numerically and its dependence on the anisotropy parameter is determined. A connection with the compounds KCuCl3, Cu2(C5H12N2)2Cl4 and (C5H12N)2CuBr4 in the strong coupling regime is made and our results for the magnetic susceptibility fit the experimental data remarkably well.Comment: 12 pages, 12 figures included, submitted to Phys. Rev.