21,731 research outputs found
Simulation of anyons with tensor network algorithms
Interacting systems of anyons pose a unique challenge to condensed matter
simulations due to their non-trivial exchange statistics. These systems are of
great interest as they have the potential for robust universal quantum
computation, but numerical tools for studying them are as yet limited. We show
how existing tensor network algorithms may be adapted for use with systems of
anyons, and demonstrate this process for the 1-D Multi-scale Entanglement
Renormalisation Ansatz (MERA). We apply the MERA to infinite chains of
interacting Fibonacci anyons, computing their scaling dimensions and local
scaling operators. The scaling dimensions obtained are seen to be in agreement
with conformal field theory. The techniques developed are applicable to any
tensor network algorithm, and the ability to adapt these ansaetze for use on
anyonic systems opens the door for numerical simulation of large systems of
free and interacting anyons in one and two dimensions.Comment: Fixed typos, matches published version. 16 pages, 21 figures, 4
tables, RevTeX 4-1. For a related work, see arXiv:1006.247
Classification of GHZ-type, W-type and GHZ-W-type multiqubit entanglements
We propose the concept of SLOCC-equivalent basis (SEB) in the multiqubit
space. In particular, two special SEBs, the GHZ-type and the W-type basis are
introduced. They can make up a more general family of multiqubit states, the
GHZ-W-type states, which is a useful kind of entanglement for quantum
teleporatation and error correction. We completely characterize the property of
this type of states, and mainly classify the GHZ-type states and the W-type
states in a regular way, which is related to the enumerative combinatorics.
Many concrete examples are given to exhibit how our method is used for the
classification of these entangled states.Comment: 16 pages, Revte
Hydrogen column density evaluations toward Capella: consequences on the interstellar deuterium abundance
The deuterium abundance evaluation in the direction of Capella has for a long
time been used as a reference for the local interstellar medium (ISM) within
our Galaxy. We show here that broad and weak HI components could be present on
the Capella line of sight, leading to a large new additional systematic
uncertainty on the N(HI) evaluation.
The D/H ratio toward Capella is found to be equal to 1.67 (+/-0.3)x10^-5 with
almost identical chi^2 for all the fits (this range includes only the
systematic error; the 2 sigma statistical one is almost negligible in
comparison). It is concluded that D/H evaluations over HI column densities
below 10^19 cm^-2 (even perhaps below 10^20 cm^-2 if demonstrated by additional
observations) may present larger uncertainties than previously anticipated. It
is mentionned that the D/O ratio might be a better tracer for DI variations in
the ISM as recently measured by the Far Ultraviolet Spectroscopic Explorer
(FUSE).Comment: Accepted for publication in the Astrophysical Journal Letter
On the energy saved by interlayer interactions in the superconducting state of cuprates
A Ginzburg-Landau-like functional is proposed reproducing the main low-energy
features of various possible high-Tc superconducting mechanisms involving
energy savings due to interlayer interactions. The functional may be used to
relate these savings to experimental quantities. Two examples are given,
involving the mean-field specific heat jump at Tc and the superconducting
fluctuations above Tc. Comparison with existing data suggests, e.g., that the
increase of Tc due to the so-called interlayer tunneling (ILT) mechanism of
interlayer kinetic-energy savings is negligible in optimally-doped Bi-2212.Comment: 12 pages, no figures. Version history: 21-aug-2003, first version
(available on http://arxiv.org/abs/cond-mat/0308423v1); 15-jan-2004, update
to match Europhys. Lett. publication (minor grammar changes, updates in
bibliography - e.g., refs. 5 and 26
Simulation of time evolution with the MERA
We describe an algorithm to simulate time evolution using the Multi-scale
Entanglement Renormalization Ansatz (MERA) and test it by studying a critical
Ising chain with periodic boundary conditions and with up to L ~ 10^6 quantum
spins. The cost of a simulation, which scales as L log(L), is reduced to log(L)
when the system is invariant under translations. By simulating an evolution in
imaginary time, we compute the ground state of the system. The errors in the
ground state energy display no evident dependence on the system size. The
algorithm can be extended to lattice systems in higher spatial dimensions.Comment: final version with data improvement (precision and size), 4.1 pages,
4 figures + extra on X
Algorithms for entanglement renormalization
We describe an iterative method to optimize the multi-scale entanglement
renormalization ansatz (MERA) for the low-energy subspace of local Hamiltonians
on a D-dimensional lattice. For translation invariant systems the cost of this
optimization is logarithmic in the linear system size. Specialized algorithms
for the treatment of infinite systems are also described. Benchmark simulation
results are presented for a variety of 1D systems, namely Ising, Potts, XX and
Heisenberg models. The potential to compute expected values of local
observables, energy gaps and correlators is investigated.Comment: 23 pages, 28 figure
How to escape Aharonov-Bohm cages ?
We study the effect of disorder and interactions on a recently proposed
magnetic field induced localization mechanism. We show that both partially
destroy the extreme confinement of the excitations occuring in the pure case
and give rise to unusual behavior. We also point out the role of the edge
states that allows for a propagation of the electrons in these systems.Comment: 22 pages, 20 EPS figure
Entanglement entropy in collective models
We discuss the behavior of the entanglement entropy of the ground state in
various collective systems. Results for general quadratic two-mode boson models
are given, yielding the relation between quantum phase transitions of the
system (signaled by a divergence of the entanglement entropy) and the
excitation energies. Such systems naturally arise when expanding collective
spin Hamiltonians at leading order via the Holstein-Primakoff mapping. In a
second step, we analyze several such models (the Dicke model, the two-level BCS
model, the Lieb-Mattis model and the Lipkin-Meshkov-Glick model) and
investigate the properties of the entanglement entropy in the whole parameter
range. We show that when the system contains gapless excitations the
entanglement entropy of the ground state diverges with increasing system size.
We derive and classify the scaling behaviors that can be met.Comment: 11 pages, 7 figure
Haffner 16: A Young Moving Group in the Making
The photometric properties of main sequence (MS) and pre-main sequence (PMS)
stars in the young cluster Haffner 16 are examined using images recorded with
the Gemini South Adaptive Optics Imager (GSAOI) and corrected for atmospheric
blurring by the Gemini Multi-Conjugate Adapative Optics System (GeMS). A rich
population of PMS stars is identified, and comparisons with isochrones suggest
an age < 10 Myr assuming a distance modulus of 13.5 (D = 5 kpc). When compared
with the solar neighborhood, Haffner 16 is roughly a factor of two deficient in
objects with sub-solar masses. PMS objects in the cluster are also more
uniformly distributed on the sky than bright MS stars. It is suggested that
Haffner 16 is dynamically evolved, and that it is shedding protostars with
sub-solar masses. Young low mass clusters like Haffner 16 are one possible
source of PMS stars in the field. The cluster will probably evolve on time
scales of ~ 100 - 1000 Myr into a diffuse moving group with a mass function
that is very different from that which prevailed early in its life.Comment: To appear in the Publications of the Astronomical Society of the
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