8,274 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
Competition between local potentials and attractive particle-particle interactions in superlattices
Naturally occuring or man-made systems displaying periodic spatial
modulations of their properties on a nanoscale constitute superlattices. Such
modulated structures are important both as prototypes of simple
nanotechnological devices and as particular examples of emerging spatial
inhomogeneity in interacting many-electron systems. Here we investigate the
effect different types of modulation of the system parameters have on the
ground-state energy and the charge-density distribution of the system. The
superlattices are described by the inhomogeneous attractive Hubbard model, and
the calculations are performed by density-functional and density-matrix
renormalization group techniques. We find that modulations in local electric
potentials are much more effective in shaping the system's properties than
modulations in the attractive on-site interaction. This is the same conclusions
we previously (Phys. Rev. B 71, 125130) obtained for repulsive interactions,
suggesting that it is not an artifact of a specific state, but a general
property of modulated structures.Comment: 8 pages, 2 figure
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
Multiperiodic magnetic structures in Hubbard superlattices
We consider fermions in one-dimensional superlattices (SL's), modeled by
site-dependent Hubbard-U couplings arranged in a repeated pattern of repulsive
(i.e., U>0) and free (U=0) sites. Density Matrix Renormalization Group (DMRG)
diagonalization of finite systems is used to calculate the local moment and the
magnetic structure factor in the ground state. We have found four regimes for
magnetic behavior: uniform local moments forming a spin-density wave (SDW),
`floppy' local moments with short-ranged correlations, local moments on
repulsive sites forming long-period SDW's superimposed with short-ranged
correlations, and local moments on repulsive sites solely with long-period
SDW's; the boundaries between these regimes depend on the range of electronic
densities, rho, and on the SL aspect ratio. Above a critical electronic
density, rho_{uparrow downarrow}, the SDW period oscillates both with rho and
with the spacer thickness. The former oscillation allows one to reproduce all
SDW wave vectors within a small range of electronic densities, unlike the
homogeneous system. The latter oscillation is related to the exchange
oscillation observed in magnetic multilayers. A crossover between regimes of
`thin' to `thick' layers has also been observed.Comment: 9 two-column pages, 10 figure
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
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