1,460 research outputs found
Comb entanglement in quantum spin chains
Bipartite entanglement in the ground state of a chain of quantum spins
can be quantified either by computing pairwise concurrence or by dividing the
chain into two complementary subsystems. In the latter case the smaller
subsystem is usually a single spin or a block of adjacent spins and the
entanglement differentiates between critical and non-critical regimes. Here we
extend this approach by considering a more general setting: our smaller
subsystem consists of a {\it comb} of spins, spaced sites apart.
Our results are thus not restricted to a simple `area law', but contain
non-local information, parameterized by the spacing . For the XX model we
calculate the von-Neumann entropy analytically when and
investigate its dependence on and . We find that an external magnetic
field induces an unexpected length scale for entanglement in this case.Comment: 6 pages, 4 figure
A new correlator in quantum spin chains
We propose a new correlator in one-dimensional quantum spin chains, the
Emptiness Formation Probability (EFP). This is a natural generalization
of the Emptiness Formation Probability (EFP), which is the probability that the
first spins of the chain are all aligned downwards. In the EFP we let
the spins in question be separated by sites. The usual EFP corresponds to
the special case when , and taking allows us to quantify non-local
correlations. We express the EFP for the anisotropic XY model in a
transverse magnetic field, a system with both critical and non-critical
regimes, in terms of a Toeplitz determinant. For the isotropic XY model we find
that the magnetic field induces an interesting length scale.Comment: 6 pages, 1 figur
On an average over the Gaussian Unitary Ensemble
We study the asymptotic limit for large matrix dimension N of the partition
function of the unitary ensemble with weight exp(-z^2/2x^2 + t/x - x^2/2). We
compute the leading order term of the partition function and of the
coefficients of its Taylor expansion. Our results are valid in the range
N^(-1/2) < z < N^(1/4). Such partition function contains all the information on
a new statistics of the eigenvalues of matrices in the Gaussian Unitary
Ensemble (GUE) that was introduced by Berry and Shukla (J. Phys. A: Math.
Theor., Vol. 41 (2008), 385202, arXiv:0807.3474). It can also be interpreted as
the moment generating function of a singular linear statistics.Comment: 28 pages, 3 figure
Synthesis and characterization of multiferroic BiMnO
We report on the high pressure synthesis of BiMnO, a manganite
displaying a "quadruple perovskite" structure. Structural characterization of
single crystal samples shows a distorted and asymmetrical coordination around
the Bi atom, due to presence of the lone pair, resulting in
non-centrosymmetric space group Im, leading to a permanent electrical dipole
moment and ferroelectric properties. On the other hand, magnetic
characterization reveals antiferromagnetic transitions, in agreement with the
isostructural compounds, thus evidencing two intrinsic properties that make
BiMnO a promising multiferroic material.Comment: 4 pages, 3 figure
Roots of the derivative of the Riemann zeta function and of characteristic polynomials
We investigate the horizontal distribution of zeros of the derivative of the
Riemann zeta function and compare this to the radial distribution of zeros of
the derivative of the characteristic polynomial of a random unitary matrix.
Both cases show a surprising bimodal distribution which has yet to be
explained. We show by example that the bimodality is a general phenomenon. For
the unitary matrix case we prove a conjecture of Mezzadri concerning the
leading order behavior, and we show that the same follows from the random
matrix conjectures for the zeros of the zeta function.Comment: 24 pages, 6 figure
Dephasing-enabled triplet Andreev conductance
We study the conductance of normal-superconducting quantum dots with strong
spin-orbit scattering, coupled to a source reservoir using a single-mode
spin-filtering quantum point contact. The choice of the system is guided by the
aim to study triplet Andreev reflection without relying on half metallic
materials with specific interface properties. Focusing on the zero temperature,
zero-bias regime, we show how dephasing due to the presence of a voltage probe
enables the conductance, which vanishes in the quantum limit, to take nonzero
values. Concentrating on chaotic quantum dots, we obtain the full distribution
of the conductance as a function of the dephasing rate. As dephasing gradually
lifts the conductance from zero, the dependence of the conductance fluctuations
on the dephasing rate is nonmonotonic. This is in contrast to chaotic quantum
dots in usual transport situations, where dephasing monotonically suppresses
the conductance fluctuations.Comment: 6 pages, 3 figure
Statistical properties of determinantal point processes in high-dimensional Euclidean spaces
The goal of this paper is to quantitatively describe some statistical
properties of higher-dimensional determinantal point processes with a primary
focus on the nearest-neighbor distribution functions. Toward this end, we
express these functions as determinants of matrices and then
extrapolate to . This formulation allows for a quick and accurate
numerical evaluation of these quantities for point processes in Euclidean
spaces of dimension . We also implement an algorithm due to Hough \emph{et.
al.} \cite{hough2006dpa} for generating configurations of determinantal point
processes in arbitrary Euclidean spaces, and we utilize this algorithm in
conjunction with the aforementioned numerical results to characterize the
statistical properties of what we call the Fermi-sphere point process for to 4. This homogeneous, isotropic determinantal point process, discussed
also in a companion paper \cite{ToScZa08}, is the high-dimensional
generalization of the distribution of eigenvalues on the unit circle of a
random matrix from the circular unitary ensemble (CUE). In addition to the
nearest-neighbor probability distribution, we are able to calculate Voronoi
cells and nearest-neighbor extrema statistics for the Fermi-sphere point
process and discuss these as the dimension is varied. The results in this
paper accompany and complement analytical properties of higher-dimensional
determinantal point processes developed in \cite{ToScZa08}.Comment: 42 pages, 17 figure
Internal-strain mediated coupling between polar Bi and magnetic Mn ions in the defect-free quadruple-perovskite BiMnMnO
By means of neutron powder diffraction, we investigated the effect of the
polar Bi ion on the magnetic ordering of the Mn ions in
BiMnMnO, the counterpart with \textit{quadruple} perovskite
structure of the \textit{simple} perovskite BiMnO. The data are consistent
with a \textit{noncentrosymmetric} spacegroup which contrasts the
\textit{centrosymmetric} one previously reported for the isovalent and
isomorphic compound LaMnMnO, which gives evidence of a
Bi-induced polarization of the lattice. At low temperature, the two
Mn sublattices of the and sites order antiferromagnetically
(AFM) in an independent manner at 25 and 55 K, similarly to the case of
LaMnMnO. However, both magnetic structures of
BiMnMnO radically differ from those of LaMnMnO.
In BiMnMnO the moments of the sites form
an anti-body AFM structure, whilst the moments \textbf{M} of the
sites result from a large and \textit{uniform} modulation along the b-axis of the moments \textbf{M} in the
-plane. The modulation is strikingly correlated with the displacements of
the Mn ions induced by the Bi ions. Our analysis unveils a strong
magnetoelastic coupling between the internal strain created by the Bi
ions and the moment of the Mn ions in the sites. This is ascribed to
the high symmetry of the oxygen sites and to the absence of oxygen defects, two
characteristics of quadruple perovskites not found in simple ones, which
prevent the release of the Bi-induced strain through distortions or
disorder. This demonstrates the possibility of a large magnetoelectric coupling
in proper ferroelectrics and suggests a novel concept of internal strain
engineering for multiferroics design.Comment: 9 pages, 7 figures, 5 table
Singling out the effect of quenched disorder in the phase diagram of cuprates
We investigate the specific influence of structural disorder on the
suppression of antiferromagnetic order and on the emergence of cuprate
superconductivity. We single out pure disorder, by focusing on a series of
YEuBaCuO samples at fixed oxygen content
, in the range . The gradual Y/Eu isovalent substitution
smoothly drives the system through the Mott-insulator to superconductor
transition from a full antiferromagnet with N\'eel transition K at
to a bulk superconductor with superconducting critical temperature
K at , YBaCuO. The electronic properties are
finely tuned by gradual lattice deformations induced by the different cationic
radii of the two lanthanides, inducing a continuous change of the basal Cu(1)-O
chain length, as well as a controlled amount of disorder in the active
Cu(2)O bilayers. We check that internal charge transfer from the basal to
the active plane is entirely responsible for the doping of the latter and we
show that superconductivity emerges with orthorhombicity. By comparing
transition temperatures with those of the isoelectronic clean system we
deterime the influence of pure structural disorder connected with the Y/Eu
alloy.Comment: 10 pages 11 figures, submitted to Journal of Physics: Condensed
Matter, Special Issue in memory of Prof. Sandro Massid
Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory
We compute the entropy of entanglement between the first spins and the
rest of the system in the ground states of a general class of quantum
spin-chains. We show that under certain conditions the entropy can be expressed
in terms of averages over ensembles of random matrices. These averages can be
evaluated, allowing us to prove that at critical points the entropy grows like
as , where and are determined explicitly. In an important class of systems,
is equal to one-third of the central charge of an associated Virasoro algebra.
Our expression for therefore provides an explicit formula for the
central charge.Comment: 4 page
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