463 research outputs found
Density Matrix Renormalization Group of Gapless Systems
We investigate convergence of the density matrix renormalization group (DMRG)
in the thermodynamic limit for gapless systems. Although the DMRG correlations
always decay exponentially in the thermodynamic limit, the correlation length
at the DMRG fixed-point scales as , where is the number
of kept states, indicating the existence of algebraic order for the exact
system. The single-particle excitation spectrum is calculated, using a
Bloch-wave ansatz, and we prove that the Bloch-wave ansatz leads to the
symmetry for translationally invariant half-integer
spin-systems with local interactions. Finally, we provide a method to compute
overlaps between ground states obtained from different DMRG calculations.Comment: 11 pages, RevTex, 5 figure
Excitation and Entanglement Transfer Near Quantum Critical Points
Recently, there has been growing interest in employing condensed matter
systems such as quantum spin or harmonic chains as quantum channels for short
distance communication. Many properties of such chains are determined by the
spectral gap between their ground and excited states. In particular this gap
vanishes at critical points of quantum phase transitions. In this article we
study the relation between the transfer speed and quality of such a system and
the size of its spectral gap. We find that the transfer is almost perfect but
slow for large spectral gaps and fast but rather inefficient for small gaps.Comment: submitted to Optics and Spectroscopy special issue for ICQO'200
Unmixing in Random Flows
We consider particles suspended in a randomly stirred or turbulent fluid.
When effects of the inertia of the particles are significant, an initially
uniform scatter of particles can cluster together. We analyse this 'unmixing'
effect by calculating the Lyapunov exponents for dense particles suspended in
such a random three-dimensional flow, concentrating on the limit where the
viscous damping rate is small compared to the inverse correlation time of the
random flow (that is, the regime of large Stokes number). In this limit
Lyapunov exponents are obtained as a power series in a parameter which is a
dimensionless measure of the inertia. We report results for the first seven
orders. The perturbation series is divergent, but we obtain accurate results
from a Pade-Borel summation. We deduce that particles can cluster onto a
fractal set and show that its dimension is in satisfactory agreement with
previously reported in simulations of turbulent Navier-Stokes flows. We also
investigate the rate of formation of caustics in the particle flow.Comment: 39 pages, 8 figure
The Dynamical Mean Field Theory phase space extension and critical properties of the finite temperature Mott transition
We consider the finite temperature metal-insulator transition in the half
filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. A
new method for calculating the Dynamical Mean Field Theory fixpoint surface in
the phase diagram is presented and shown to be free from the convergence
problems of standard forward recursion. The fixpoint equation is then analyzed
using dynamical systems methods. On the fixpoint surface the eigenspectra of
its Jacobian is used to characterize the hysteresis boundaries of the first
order transition line and its second order critical end point. The critical
point is shown to be a cusp catastrophe in the parameter space, opening a
pitchfork bifurcation along the first order transition line, while the
hysteresis boundaries are shown to be saddle-node bifurcations of two merging
fixpoints. Using Landau theory the properties of the critical end point is
determined and related to the critical eigenmode of the Jacobian. Our findings
provide new insights into basic properties of this intensively studied
transition.Comment: 11 pages, 12 figures, 1 tabl
Clustering in mixing flows
We calculate the Lyapunov exponents for particles suspended in a random
three-dimensional flow, concentrating on the limit where the viscous damping
rate is small compared to the inverse correlation time. In this limit Lyapunov
exponents are obtained as a power series in epsilon, a dimensionless measure of
the particle inertia. Although the perturbation generates an asymptotic series,
we obtain accurate results from a Pade-Borel summation. Our results prove that
particles suspended in an incompressible random mixing flow can show pronounced
clustering when the Stokes number is large and we characterise two distinct
clustering effects which occur in that limit.Comment: 5 pages, 1 figur
Landau Ginzburg theory of the d-wave Josephson junction
This letter discusses the Landau Ginzburg theory of a Josephson junction
composed of on one side a pure d-wave superconductor oriented with the
axis normal to the junction and on the other side either s-wave or d-wave
oriented with normal to the junction. We use simple symmetry arguments
to show that the Josephson current as a function of the phase must have the
form . In principle vanishes
for a perfect junction of this type, but anisotropy effects, either due to a-b
axis asymmetry or junction imperfections can easily cause to be
quite large even in a high quality junction. If is sufficiently
small and is negative local time reversal symmetry breaking will appear.
Arbitrary values of the flux would then be pinned to corners between such
junctions and occasionally on junction faces, which is consistent with
experiments by Kirtley et al
Superconductivity in hole-doped C60 from electronic correlations
We derive a model for the highest occupied molecular orbital band of a C60
crystal which includes on-site electron-electron interactions. The form of the
interactions are based on the icosahedral symmetry of the C60 molecule together
with a perturbative treatment of an isolated C60 molecule. Using this model we
do a mean-field calculation in two dimensions on the [100] surface of the
crystal. Due to the multi-band nature we find that electron-electron
interactions can have a profound effect on the density of states as a function
of doping. The doping dependence of the transition temperature can then be
qualitatively different from that expected from simple BCS theory based on the
density of states from band structure calculations
Numerical Renormalization Group at Criticality
We apply a recently developed numerical renormalization group, the
corner-transfer-matrix renormalization group (CTMRG), to 2D classical lattice
models at their critical temperatures. It is shown that the combination of
CTMRG and the finite-size scaling analysis gives two independent critical
exponents.Comment: 5 pages, LaTeX, 5 figures available upon reques
Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
The density matrix renormalization group (``DMRG'') discovered by White has
shown to be a powerful method to understand the properties of many one
dimensional quantum systems. In the case where renormalization eventually
converges to a fixed point we show that quantum states in the thermodynamic
limit with periodic boundary conditions can be simply represented by a special
type of product ground state with a natural description of Bloch states of
elementary excitations that are spin-1 solitons. We then observe that these
states can be rederived through a simple variational ansatz making no reference
to a renormalization construction. The method is tested on the spin-1
Heisenberg model.Comment: 13 pages uuencoded compressed postscript including figure
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