201 research outputs found
Towards Multi-Scale Modeling of Carbon Nanotube Transistors
Multiscale simulation approaches are needed in order to address scientific
and technological questions in the rapidly developing field of carbon nanotube
electronics. In this paper, we describe an effort underway to develop a
comprehensive capability for multiscale simulation of carbon nanotube
electronics. We focus in this paper on one element of that hierarchy, the
simulation of ballistic CNTFETs by self-consistently solving the Poisson and
Schrodinger equations using the non-equilibrium Greens function (NEGF)
formalism. The NEGF transport equation is solved at two levels: i) a
semi-empirical atomistic level using the pz orbitals of carbon atoms as the
basis, and ii) an atomistic mode space approach, which only treats a few
subbands in the tube-circumferential direction while retaining an atomistic
grid along the carrier transport direction. Simulation examples show that these
approaches describe quantum transport effects in nanotube transistors. The
paper concludes with a brief discussion of how these semi-empirical device
level simulations can be connected to ab initio, continuum, and circuit level
simulations in the multi-scale hierarchy
Diagnosing Potts criticality and two-stage melting in one-dimensional hard-boson models
We investigate a model of hard-core bosons with infinitely repulsive nearest-
and next-nearest-neighbor interactions in one dimension, introduced by Fendley,
Sengupta and Sachdev in Phys. Rev. B 69, 075106 (2004). Using a combination of
exact diagonalization, tensor network, and quantum Monte Carlo simulations, we
show how an intermediate incommensurate phase separates a crystalline and a
disordered phase. We base our analysis on a variety of diagnostics, including
entanglement measures, fidelity susceptibility, correlation functions, and
spectral properties. According to theoretical expectations, the
disordered-to-incommensurate-phase transition point is compatible with
Berezinskii-Kosterlitz-Thouless universal behaviour. The second transition is
instead non-relativistic, with dynamical critical exponent . For the
sake of comparison, we illustrate how some of the techniques applied here work
at the Potts critical point present in the phase diagram of the model for
finite next-nearest-neighbor repulsion. This latter application also allows to
quantitatively estimate which system sizes are needed to match the conformal
field theory spectra with experiments performing level spectroscopy.Comment: 18 pages, 14 figure
The Geometry of Niggli Reduction II: BGAOL -- Embedding Niggli Reduction
Niggli reduction can be viewed as a series of operations in a six-dimensional
space derived from the metric tensor. An implicit embedding of the space of
Niggli-reduced cells in a higher dimensional space to facilitate calculation of
distances between cells is described. This distance metric is used to create a
program, BGAOL, for Bravais lattice determination. Results from BGAOL are
compared to the results from other metric-based Bravais lattice determination
algorithms
The Flat Phase of Crystalline Membranes
We present the results of a high-statistics Monte Carlo simulation of a
phantom crystalline (fixed-connectivity) membrane with free boundary. We verify
the existence of a flat phase by examining lattices of size up to . The
Hamiltonian of the model is the sum of a simple spring pair potential, with no
hard-core repulsion, and bending energy. The only free parameter is the the
bending rigidity . In-plane elastic constants are not explicitly
introduced. We obtain the remarkable result that this simple model dynamically
generates the elastic constants required to stabilise the flat phase. We
present measurements of the size (Flory) exponent and the roughness
exponent . We also determine the critical exponents and
describing the scale dependence of the bending rigidity () and the induced elastic constants (). At bending rigidity , we find
(Hausdorff dimension ), and . These results are consistent with the scaling relation . The additional scaling relation implies
. A direct measurement of from the power-law decay of
the normal-normal correlation function yields on the
lattice.Comment: Latex, 31 Pages with 14 figures. Improved introduction, appendix A
and discussion of numerical methods. Some references added. Revised version
to appear in J. Phys.
Commensurate lock-in and incommensurate supersolid phases of hardcore bosons on anisotropic triangular lattices
We investigate the interplay between commensurate lock-in and incommensurate
supersolid phases of the hardcore bosons at half-filling with anisotropic
nearest-neighbor hopping and repulsive interactions on triangular lattice. We
use numerical quantum and variational Monte Carlo as well as analytical
Schwinger boson mean-field analysis to establish the ground states and phase
diagram. It is shown that, for finite size systems, there exist a series of
jumps between different supersolid phases as the anisotropy parameter is
changed. The density ordering wavevectors are locked to commensurate values and
jump between adjacent supersolids. In the thermodynamic limit, however, the
magnitude of these jumps vanishes leading to a continuous set of novel
incommensurate supersoild phases.Comment: 5 pages, 5 figures, added new results, changed title and conclusio
Area laws for the entanglement entropy - a review
Physical interactions in quantum many-body systems are typically local:
Individual constituents interact mainly with their few nearest neighbors. This
locality of interactions is inherited by a decay of correlation functions, but
also reflected by scaling laws of a quite profound quantity: The entanglement
entropy of ground states. This entropy of the reduced state of a subregion
often merely grows like the boundary area of the subregion, and not like its
volume, in sharp contrast with an expected extensive behavior. Such "area laws"
for the entanglement entropy and related quantities have received considerable
attention in recent years. They emerge in several seemingly unrelated fields,
in the context of black hole physics, quantum information science, and quantum
many-body physics where they have important implications on the numerical
simulation of lattice models. In this Colloquium we review the current status
of area laws in these fields. Center stage is taken by rigorous results on
lattice models in one and higher spatial dimensions. The differences and
similarities between bosonic and fermionic models are stressed, area laws are
related to the velocity of information propagation, and disordered systems,
non-equilibrium situations, classical correlation concepts, and topological
entanglement entropies are discussed. A significant proportion of the article
is devoted to the quantitative connection between the entanglement content of
states and the possibility of their efficient numerical simulation. We discuss
matrix-product states, higher-dimensional analogues, and states from
entanglement renormalization and conclude by highlighting the implications of
area laws on quantifying the effective degrees of freedom that need to be
considered in simulations.Comment: 28 pages, 2 figures, final versio
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