28 research outputs found
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
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
Superfluid, Mott-Insulator, and Mass-Density-Wave Phases in the One-Dimensional Extended Bose-Hubbard Model
We use the finite-size density-matrix-renormalization-group (FSDMRG) method
to obtain the phase diagram of the one-dimensional () extended
Bose-Hubbard model for density in the plane, where and
are, respectively, onsite and nearest-neighbor interactions. The phase diagram
comprises three phases: Superfluid (SF), Mott Insulator (MI) and Mass Density
Wave (MDW). For small values of and , we get a reentrant SF-MI-SF phase
transition. For intermediate values of interactions the SF phase is sandwiched
between MI and MDW phases with continuous SF-MI and SF-MDW transitions. We
show, by a detailed finite-size scaling analysis, that the MI-SF transition is
of Kosterlitz-Thouless (KT) type whereas the MDW-SF transition has both KT and
two-dimensional-Ising characters. For large values of and we get a
direct, first-order, MI-MDW transition. The MI-SF, MDW-SF and MI-MDW phase
boundaries join at a bicritical point at (.Comment: 10 pages, 15 figure
Photoinduced charge and spin dynamics in strongly correlated electron systems
Motivated by photoinduced phase transition in manganese oxides, charge and
spin dynamics induced by photoirradiation are examined. We calculate the
transient optical absorption spectra of the extended double-exchange model by
the density matrix renormalization group (DMRG) method. A charge-ordered
insulating (COI) state becomes metallic just after photoirradiation, and the
system tends to recover the initial COI state. The recovery is accompanied with
remarkable suppression of an antiferromagnetic correlation in the COI state.
The DMRG results are consistent with recent pump-probe spectroscopy data.Comment: 5 pages, 4 figure
The density-matrix renormalization group
The density-matrix renormalization group (DMRG) is a numerical algorithm for
the efficient truncation of the Hilbert space of low-dimensional strongly
correlated quantum systems based on a rather general decimation prescription.
This algorithm has achieved unprecedented precision in the description of
one-dimensional quantum systems. It has therefore quickly acquired the status
of method of choice for numerical studies of one-dimensional quantum systems.
Its applications to the calculation of static, dynamic and thermodynamic
quantities in such systems are reviewed. The potential of DMRG applications in
the fields of two-dimensional quantum systems, quantum chemistry,
three-dimensional small grains, nuclear physics, equilibrium and
non-equilibrium statistical physics, and time-dependent phenomena is discussed.
This review also considers the theoretical foundations of the method, examining
its relationship to matrix-product states and the quantum information content
of the density matrices generated by DMRG.Comment: accepted by Rev. Mod. Phys. in July 2004; scheduled to appear in the
January 2005 issu
Optical conductivity of the half-filled Hubbard chain
We combine well-controlled analytical and numerical methods to determine the
optical conductivity of the one-dimensional Mott-Hubbard insulator at zero
temperature. A dynamical density-matrix renormalization group method provides
the entire absorption spectrum for all but very small coupling strengths. In
this limit we calculate the conductivity analytically using exact
field-theoretical methods. Above the Lieb-Wu gap the conductivity exhibits a
characteristic square-root increase. For small to moderate interactions, a
sharp maximum occurs just above the gap. For larger interactions, another weak
feature becomes visible around the middle of the absorption band.Comment: 4 pages with 3 eps figures, published version (changes in text and
references
Excitons in one-dimensional Mott insulators
We employ dynamical density-matrix renormalization group (DDMRG) and
field-theory methods to determine the frequency-dependent optical conductivity
in one-dimensional extended, half-filled Hubbard models. The field-theory
approach is applicable to the regime of `small' Mott gaps which is the most
difficult to access by DDMRG. For very large Mott gaps the DDMRG recovers
analytical results obtained previously by means of strong-coupling techniques.
We focus on exciton formation at energies below the onset of the absorption
continuum. As a consequence of spin-charge separation, these Mott-Hubbard
excitons are bound states of spinless, charged excitations (`holon-antiholon'
pairs). We also determine exciton binding energies and sizes. In contrast to
simple band insulators, we observe that excitons exist in the Mott-insulating
phase only for a sufficiently strong intersite Coulomb repulsion. Furthermore,
our results show that the exciton binding energy and size are not related in a
simple way to the strength of the Coulomb interaction.Comment: 15 pages, 6 eps figures, corrected typos in labels of figures 4,5,
and
Density-matrix renormalisation group approach to quantum impurity problems
A dynamic density-matrix renormalisation group approach to the spectral
properties of quantum impurity problems is presented. The method is
demonstrated on the spectral density of the flat-band symmetric single-impurity
Anderson model. We show that this approach provides the impurity spectral
density for all frequencies and coupling strengths. In particular, Hubbard
satellites at high energy can be obtained with a good resolution. The main
difficulties are the necessary discretisation of the host band hybridised with
the impurity and the resolution of sharp spectral features such as the
Abrikosov-Suhl resonance.Comment: 16 pages, 6 figures, submitted to Journal of Physics: Condensed
Matte
Phases of the one-dimensional Bose-Hubbard model
The zero-temperature phase diagram of the one-dimensional Bose-Hubbard model
with nearest-neighbor interaction is investigated using the Density-Matrix
Renormalization Group. Recently normal phases without long-range order have
been conjectured between the charge density wave phase and the superfluid phase
in one-dimensional bosonic systems without disorder. Our calculations
demonstrate that there is no intermediate phase in the one-dimensional
Bose-Hubbard model but a simultaneous vanishing of crystalline order and
appearance of superfluid order. The complete phase diagrams with and without
nearest-neighbor interaction are obtained. Both phase diagrams show reentrance
from the superfluid phase to the insulator phase.Comment: Revised version, 4 pages, 5 figure
Metal-insulator transition in the one-dimensional Holstein model at half filling
We study the one-dimensional Holstein model with spin-1/2 electrons at
half-filling. Ground state properties are calculated for long chains with great
accuracy using the density matrix renormalization group method and extrapolated
to the thermodynamic limit. We show that for small electron-phonon coupling or
large phonon frequency, the insulating Peierls ground state predicted by
mean-field theory is destroyed by quantum lattice fluctuations and that the
system remains in a metallic phase with a non-degenerate ground state and
power-law electronic and phononic correlations. When the electron-phonon
coupling becomes large or the phonon frequency small, the system undergoes a
transition to an insulating Peierls phase with a two-fold degenerate ground
state, long-range charge-density-wave order, a dimerized lattice structure, and
a gap in the electronic excitation spectrum.Comment: 6 pages (LaTex), 10 eps figure