6,874 research outputs found
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 can simulate, cancel, or even
overcompensate effects due to much larger variations in the on-site interaction
. 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 for and . 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.
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.
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