2,034 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
Optimal Nonlinear Eddy Viscosity in Galerkin Models of Turbulent Flows
We propose a variational approach to identification of an optimal nonlinear
eddy viscosity as a subscale turbulence representation for POD models. The
ansatz for the eddy viscosity is given in terms of an arbitrary function of the
resolved fluctuation energy. This function is found as a minimizer of a cost
functional measuring the difference between the target data coming from a
resolved direct or large-eddy simulation of the flow and its reconstruction
based on the POD model. The optimization is performed with a data-assimilation
approach generalizing the 4D-VAR method. POD models with optimal eddy
viscosities are presented for a 2D incompressible mixing layer at
(based on the initial vorticity thickness and the velocity of the high-speed
stream) and a 3D Ahmed body wake at (based on the body height and
the free-stream velocity). The variational optimization formulation elucidates
a number of interesting physical insights concerning the eddy-viscosity ansatz
used. The 20-dimensional model of the mixing-layer reveals a negative
eddy-viscosity regime at low fluctuation levels which improves the transient
times towards the attractor. The 100-dimensional wake model yields more
accurate energy distributions as compared to the nonlinear modal eddy-viscosity
benchmark {proposed recently} by \"Osth et al. (2014). Our methodology can be
applied to construct quite arbitrary closure relations and, more generally,
constitutive relations optimizing statistical properties of a broad class of
reduced-order models.Comment: 41 pages, 16 figures; accepted for publication in Journal of Fluid
Mechanic
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