4,043 research outputs found

### Gapped and gapless phases of frustration-free spin-1/2 chains

We consider a family of translation-invariant quantum spin chains with
nearest-neighbor interactions and derive necessary and sufficient conditions
for these systems to be gapped in the thermodynamic limit. More precisely, let
$\psi$ be an arbitrary two-qubit state. We consider a chain of $n$ qubits with
open boundary conditions and Hamiltonian $H_n(\psi)$ which is defined as the
sum of rank-1 projectors onto $\psi$ applied to consecutive pairs of qubits. We
show that the spectral gap of $H_n(\psi)$ is upper bounded by $1/(n-1)$ if the
eigenvalues of a certain two-by-two matrix simply related to $\psi$ have equal
non-zero absolute value. Otherwise, the spectral gap is lower bounded by a
positive constant independent of $n$ (depending only on $\psi$). A key
ingredient in the proof is a new operator inequality for the ground space
projector which expresses a monotonicity under the partial trace. This
monotonicity property appears to be very general and might be interesting in
its own right. As an extension of our main result, we obtain a complete
classification of gapped and gapless phases of frustration-free
translation-invariant spin-1/2 chains with nearest-neighbor interactions.Comment: v3: published versio

### The X-ray light curve of the massive colliding wind Wolf-Rayet + O binary WR21a

Our dedicated XMM-Newton monitoring, as well as archival Chandra and Swift
datasets, were used to examine the behaviour of the WN5h+O3V binary WR21a at
high energies. For most of the orbit, the X-ray emission exhibits few
variations. However, an increase in strength of the emission is seen before
periastron, following a 1/D relative trend, where D is the separation between
both components. This increase is rapidly followed by a decline due to strong
absorption as the Wolf-Rayet (WR) comes in front. The fitted local absorption
value appears to be coherent with a mass-loss rate of about 1x10^{-5} M_sol/yr
for the WR component. However, absorption is not the only parameter affecting
the X-ray emission at periastron as even the hard X-ray emission decreases,
suggesting a possible collapse of the colliding wind region near to or onto the
photosphere of the companion just before or at periastron. An eclipse may
appear as another potential scenario, but it would be in apparent contradiction
with several lines of evidence, notably the width of the dip in the X-ray light
curve and the absence of variations in the UV light curve. Afterwards, the
emission slowly recovers, with a strong hysteresis effect. The observed
behaviour is compatible with predictions from general wind-wind collision
models although the absorption increase is too shallow.Comment: Accepted for publication in Astronomy & Astrophysic

### Complexity of the XY antiferromagnet at fixed magnetization

We prove that approximating the ground energy of the antiferromagnetic XY
model on a simple graph at fixed magnetization (given as part of the instance
specification) is QMA-complete. To show this, we strengthen a previous result
by establishing QMA-completeness for approximating the ground energy of the
Bose-Hubbard model on simple graphs. Using a connection between the XY and
Bose-Hubbard models that we exploited in previous work, this establishes
QMA-completeness of the XY model

### Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets

We generalize an efficient exact synthesis algorithm for single-qubit
unitaries over the Clifford+T gate set which was presented by Kliuchnikov,
Maslov and Mosca. Their algorithm takes as input an exactly synthesizable
single-qubit unitary--one which can be expressed without error as a product of
Clifford and T gates--and outputs a sequence of gates which implements it. The
algorithm is optimal in the sense that the length of the sequence, measured by
the number of T gates, is smallest possible. In this paper, for each positive
even integer $n$ we consider the "Clifford-cyclotomic" gate set consisting of
the Clifford group plus a z-rotation by $\frac{\pi}{n}$. We present an
efficient exact synthesis algorithm which outputs a decomposition using the
minimum number of $\frac{\pi}{n}$ z-rotations. For the Clifford+T case $n=4$
the group of exactly synthesizable unitaries was shown to be equal to the group
of unitaries with entries over the ring $\mathbb{Z}[e^{i\frac{\pi}{n}},1/2]$.
We prove that this characterization holds for a handful of other small values
of $n$ but the fraction of positive even integers for which it fails to hold is
100%.Comment: v2: published versio

### An exceptional X-ray view of the young open cluster NGC 6231: what XMM-Newton has taught us

Considered as the core of the Sco OB1 association, the young open cluster NGC
6231 harbours a rich O-type star population. In 2001, the XMM-Newton satellite
targeted the cluster for a nominal duration of about 180 ks. Thanks to the
detector sensitivity, the EPIC cameras provided an unprecedented X-ray view of
NGC 6231, revealing about 600 point-like sources. In this contribution, we
review the main results that have been obtained thanks to this unprecedented
data set. Concerning the O-type stars, we present the latest developments
related to the so-called 'canonical' Lx-Lbol relation. The dispersion around
this relation might actually be much smaller than previously thought. In our
data set, the sole mechanism that yields a significant deviation from this
scheme is wind interaction. It is also the sole mechanism that induces a
significant variation of the early-type star X-ray flux. In a second part of
this contribution, we probe the properties of the optically faint X-ray
sources. Most of them are believed to be low mass pre-main sequence stars.
Their analysis provides direct insight into the star formation history of the
cluster.Comment: 6 pages, 5 figures, to appear in "The X-Ray Universe 2005", ESA
Symposium held at El Escorial, Madrid (Spain), 26-30 Sep 200

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