1,520 research outputs found
The Doped Two Chain Hubbard Model
The properties of the two-chain Hubbard Model doped away from half-filling
are investigated. The charge gap is found to vanish, but a finite spin gap
exists over a range of interchain hopping strength . In this range,
there are modified --like pairing correlations whose strength is
correlated with the size of the spin gap. It is found that the pair field
correlations are enhanced by the onsite Coulomb interaction U.Comment: 10 pages and 5 postscript figures, RevTeX 3.0, UCI-CMTHE-94-0
On the dimerized phase in the cross-coupled antiferromagnetic spin ladder
We revisit the phase diagram of the frustrated s=1/2 spin ladder with
antiferromagnetic rung and diagonal couplings. In particular, we reexamine the
evidence for the columnar dimer phase, which has been predicted from analytic
treatment of the model and has been claimed to be found in numerical
calculations. By considering longer chains and by keeping more states than in
previous work using the density-matrix renormalization group, we show that the
numerical evidence presented previously for the existence of the dimerized
phase is not unambiguous in view of the present more careful analysis. While we
cannot completely rule out the possibility of a dimerized phase in the
cross-coupled ladder, we do set limits on the maximum possible value of the
dimer order parameter that are much smaller than those found previously.Comment: 6 pages, 7 figure
Quantum information analysis of the phase diagram of the half-filled extended Hubbard model
We examine the phase diagram of the half-filled one-dimensional extended
Hubbard model using quantum information entropies within the density-matrix
renormalization group. It is well known that there is a charge-density-wave
phase at large nearest-neighbor and small on-site Coloumb repulsion and a
spin-density-wave at small nearest-neighbor and large on-site Coloumb
repulsion. At intermediate Coulomb interaction strength, we find an additional
narrow region of a bond-order phase between these two phases. The phase
transition line for the transition out of the charge-density-wave phase changes
from first-order at strong coupling to second-order in a parameter regime where
all three phases are present. We present evidence that the additional
phase-transition line between the spin-density-wave and bond-order phases is
infinite order. While these results are in agreement with recent numerical
work, our study provides an independent, unbiased means of determining the
phase boundaries by using quantum information analysis, yields values for the
location of some of the phase boundaries that differ from those previously
found, and provides insight into the limitations of numerical methods in
determining phase boundaries, especially those of infinite-order transitions.Comment: 8 pages, 7 figure
Diagonalization- and Numerical Renormalization-Group-Based Methods for Interacting Quantum Systems
In these lecture notes, we present a pedagogical review of a number of
related {\it numerically exact} approaches to quantum many-body problems. In
particular, we focus on methods based on the exact diagonalization of the
Hamiltonian matrix and on methods extending exact diagonalization using
renormalization group ideas, i.e., Wilson's Numerical Renormalization Group
(NRG) and White's Density Matrix Renormalization Group (DMRG). These methods
are standard tools for the investigation of a variety of interacting quantum
systems, especially low-dimensional quantum lattice models. We also survey
extensions to the methods to calculate properties such as dynamical quantities
and behavior at finite temperature, and discuss generalizations of the DMRG
method to a wider variety of systems, such as classical models and quantum
chemical problems. Finally, we briefly review some recent developments for
obtaining a more general formulation of the DMRG in the context of matrix
product states as well as recent progress in calculating the time evolution of
quantum systems using the DMRG and the relationship of the foundations of the
method with quantum information theory.Comment: 51 pages; lecture notes on numerically exact methods. Pedagogical
review appearing in the proceedings of the "IX. Training Course in the
Physics of Correlated Electron Systems and High-Tc Superconductors", Vietri
sul Mare (Salerno, Italy, October 2004
Random dispersion approximation for the Hubbard model
We use the Random Dispersion Approximation (RDA) to study the Mott-Hubbard
transition in the Hubbard model at half band filling. The RDA becomes exact for
the Hubbard model in infinite dimensions. We implement the RDA on finite chains
and employ the Lanczos exact diagonalization method in real space to calculate
the ground-state energy, the average double occupancy, the charge gap, the
momentum distribution, and the quasi-particle weight. We find a satisfactory
agreement with perturbative results in the weak- and strong-coupling limits. A
straightforward extrapolation of the RDA data for lattice results in
a continuous Mott-Hubbard transition at . We discuss the
significance of a possible signature of a coexistence region between insulating
and metallic ground states in the RDA that would correspond to the scenario of
a discontinuous Mott-Hubbard transition as found in numerical investigations of
the Dynamical Mean-Field Theory for the Hubbard model.Comment: 10 pages, 11 figure
Magnetism of one-dimensional Wigner lattices and its impact on charge order
The magnetic phase diagram of the quarter-filled generalized Wigner lattice
with nearest- and next-nearest-neighbor hopping t_1 and t_2 is explored. We
find a region at negative t_2 with fully saturated ferromagnetic ground states
that we attribute to kinetic exchange. Such interaction disfavors
antiferromagnetism at t_2 <0 and stems from virtual excitations across the
charge gap of the Wigner lattice, which is much smaller than the Mott-Hubbard
gap proportional to U. Remarkably, we find a strong dependence of the charge
structure factor on magnetism even in the limit U to infinity, in contrast to
the expectation that charge ordering in the Wigner lattice regime should be
well described by spinless fermions. Our results, obtained using the
density-matrix renormalization group and exact diagonalization, can be
transparently explained by means of an effective low-energy Hamiltonian
Uniform and staggered magnetizations induced by Dzyaloshinskii-Moriya interactions in isolated and coupled spin 1/2 dimers in a magnetic field
We investigate the interplay of Dzyaloshinskii-Moriya interactions and an
external field in spin 1/2 dimers. For isolated dimers and at low field, we
derive simple expressions for the staggered and uniform magnetizations which
show that the orientation of the uniform magnetization can deviate
significantly from that of the external field. In fact, in the limit where the
vector of the Dzyaloshinskii-Moriya interaction is parallel to the
external field, the uniform magnetization actually becomes {\it perpendicular}
to the field. For larger fields, we show that the staggered magnetization of an
isolated dimer has a maximum close to one-half the polarization, with a large
maximal value of in the limit of very small Dzyaloshinskii-Moriya
interaction. We investigate the effect of inter-dimer coupling in the context
of ladders with Density Matrix Renormalization Group (DMRG) calculations and
show that, as long as the values of the Dzyaloshinskii-Moriya and of the
exchange interaction are compatible with respect to the development of a
staggered magnetization, the simple picture that emerges for isolated dimers is
also valid for weakly coupled dimers with minor modifications. The results are
compared with torque measurements on
Cu(CHN)Cl.Comment: 8 pages, 9 figure
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