4,465 research outputs found
Quantum Belief Propagation
We present an accurate numerical algorithm, called quantum belief propagation
(QBP), for simulation of one-dimensional quantum systems at non-zero
temperature. The algorithm exploits the fact that quantum effects are
short-range in these systems at non-zero temperature, decaying on a length
scale inversely proportional to the temperature. We compare to exact results on
a spin-1/2 Heisenberg chain. Even a very modest calculation, requiring
diagonalizing only 10-by-10 matrices, reproduces the peak susceptibility with a
relative error of less than , while more elaborate calculations
further reduce the error.Comment: 4 pages, 1 figure; revised time estimates due to improved
implementation. Typographical corrections to Eq. 7 made; thanks to David
Poulin for pointing out the mistak
Disordered Topological Insulators via -Algebras
The theory of almost commuting matrices can be used to quantify topological
obstructions to the existence of localized Wannier functions with time-reversal
symmetry in systems with time-reversal symmetry and strong spin-orbit coupling.
We present a numerical procedure that calculates a Z_2 invariant using these
techniques, and apply it to a model of HgTe. This numerical procedure allows us
to access sizes significantly larger than procedures based on studying twisted
boundary conditions. Our numerical results indicate the existence of a metallic
phase in the presence of scattering between up and down spin components, while
there is a sharp transition when the system decouples into two copies of the
quantum Hall effect. In addition to the Z_2 invariant calculation in the case
when up and down components are coupled, we also present a simple method of
evaluating the integer invariant in the quantum Hall case where they are
decoupled.Comment: Added detail regarding the mapping of almost commuting unitary
matrices to almost commuting Hermitian matrices that form an approximate
representation of the sphere. 6 pages, 6 figure
Fractal to Nonfractal Phase Transition in the Dielectric Breakdown Model
A fast method is presented for simulating the dielectric-breakdown model
using iterated conformal mappings. Numerical results for the dimension and for
corrections to scaling are in good agreement with the recent RG prediction of
an upper critical , at which a transition occurs between branching
fractal clusters and one-dimensional nonfractal clusters.Comment: 5 pages, 7 figures; corrections to scaling include
EAGLE ISS - A modular twin-channel integral-field near-IR spectrograph
The ISS (Integral-field Spectrograph System) has been designed as part of the
EAGLE Phase A Instrument Study for the E-ELT. It consists of two input channels
of 1.65x1.65 arcsec field-of-view, each reconfigured spatially by an
image-slicing integral-field unit to feed a single near-IR spectrograph using
cryogenic volume-phase-holographic (VPH) gratings to disperse the image
spectrally. A 4k x 4k array detector array records the dispersed images. The
optical design employs anamorphic magnification, image slicing, VPH gratings
scanned with a novel cryo-mechanism and a three-lens camera. The mechanical
implementation features IFU optics in Zerodur, a modular bench structure and a
number of high-precision cryo-mechanisms.Comment: 12 pages, to be published in Proc SPIE 7735: Ground-based & Airborne
Instrumentation for Astronomy II
Anomalies in the Entanglement Properties of the Square Lattice Heisenberg Model
We compute the bipartite entanglement properties of the spin-half
square-lattice Heisenberg model by a variety of numerical techniques that
include valence bond quantum Monte Carlo (QMC), stochastic series expansion
QMC, high temperature series expansions and zero temperature coupling constant
expansions around the Ising limit. We find that the area law is always
satisfied, but in addition to the entanglement entropy per unit boundary
length, there are other terms that depend logarithmically on the subregion
size, arising from broken symmetry in the bulk and from the existence of
corners at the boundary. We find that the numerical results are anomalous in
several ways. First, the bulk term arising from broken symmetry deviates from
an exact calculation that can be done for a mean-field Neel state. Second, the
corner logs do not agree with the known results for non-interacting Boson
modes. And, third, even the finite temperature mutual information shows an
anomalous behavior as T goes to zero, suggesting that T->0 and L->infinity
limits do not commute. These calculations show that entanglement entropy
demonstrates a very rich behavior in d>1, which deserves further attention.Comment: 12 pages, 7 figures, 2 tables. Numerical values in Table I correcte
Nonlinear dynamics, rectification, and phase locking for particles on symmetrical two-dimensional periodic substrates with dc and circular ac drives
We investigate the dynamical motion of particles on a two-dimensional
symmetric periodic substrate in the presence of both a dc drive along a
symmetry direction of the periodic substrate and an additional circular ac
drive. For large enough ac drives, the particle orbit encircles one or more
potential maxima of the periodic substrate. In this case, when an additional
increasing dc drive is applied in the longitudinal direction, the longitudinal
velocity increases in a series of discrete steps that are integer multiples of
the lattice constant of the substrate times the frequency. Fractional steps can
also occur. These integer and fractional steps correspond to distinct stable
dynamical orbits. A number of these phases also show a rectification in the
positive or negative transverse direction where a non-zero transverse velocity
occurs in the absence of a dc transverse drive. We map out the phase diagrams
of the regions of rectification as a function of ac amplitude, and find a
series of tongues. Most of the features, including the steps in the
longitudinal velocity and the transverse rectification, can be captured with a
simple toy model and by arguments from nonlinear maps. We have also
investigated the effects of thermal disorder and incommensuration on the
rectification phenomena, and find that for increasing disorder, the
rectification regions are gradually smeared and the longitudinal velocity steps
are no longer flat but show a linearly increasing velocity.Comment: 14 pages, 17 postscript figure
Random Vibrational Networks and Renormalization Group
We consider the properties of vibrational dynamics on random networks, with
random masses and spring constants. The localization properties of the
eigenstates contrast greatly with the Laplacian case on these networks. We
introduce several real-space renormalization techniques which can be used to
describe this dynamics on general networks, drawing on strong disorder
techniques developed for regular lattices. The renormalization group is capable
of elucidating the localization properties, and provides, even for specific
network instances, a fast approximation technique for determining the spectra
which compares well with exact results.Comment: 4 pages, 3 figure
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