1,288 research outputs found
On the continuum limit of the entanglement Hamiltonian
We consider the entanglement Hamiltonian for an interval in a chain of free fermions in its ground state and show that the lattice expression goes over into the conformal one if one includes the hopping to distant neighbours in the continuum limit. For an infinite chain, this can be done analytically for arbitrary fillings and is shown to be the consequence of the particular structure of the entanglement Hamiltonian, while for finite rings or temperatures the result is based on numerical calculations
Entanglement in the XX spin chain with an energy current
We consider the ground state of the XX chain that is constrained to carry a
current of energy. The von Neumann entropy of a block of neighboring spins,
describing entanglement of the block with the rest of the chain, is computed.
Recent calculations have revealed that the entropy in the XX model diverges
logarithmically with the size of the subsystem. We show that the presence of
the energy current increases the prefactor of the logarithmic growth. This
result indicates that the emergence of the energy current gives rise to an
increase of entanglement.Comment: 4 pages, 4 figure
Observations Outside the Light-Cone: Algorithms for Non-Equilibrium and Thermal States
We apply algorithms based on Lieb-Robinson bounds to simulate time-dependent
and thermal quantities in quantum systems. For time-dependent systems, we
modify a previous mapping to quantum circuits to significantly reduce the
computer resources required. This modification is based on a principle of
"observing" the system outside the light-cone. We apply this method to study
spin relaxation in systems started out of equilibrium with initial conditions
that give rise to very rapid entanglement growth. We also show that it is
possible to approximate time evolution under a local Hamiltonian by a quantum
circuit whose light-cone naturally matches the Lieb-Robinson velocity.
Asymptotically, these modified methods allow a doubling of the system size that
one can obtain compared to direct simulation. We then consider a different
problem of thermal properties of disordered spin chains and use quantum belief
propagation to average over different configurations. We test this algorithm on
one dimensional systems with mixed ferromagnetic and anti-ferromagnetic bonds,
where we can compare to quantum Monte Carlo, and then we apply it to the study
of disordered, frustrated spin systems.Comment: 19 pages, 12 figure
The components of empirical multifractality in financial returns
We perform a systematic investigation on the components of the empirical
multifractality of financial returns using the daily data of Dow Jones
Industrial Average from 26 May 1896 to 27 April 2007 as an example. The
temporal structure and fat-tailed distribution of the returns are considered as
possible influence factors. The multifractal spectrum of the original return
series is compared with those of four kinds of surrogate data: (1) shuffled
data that contain no temporal correlation but have the same distribution, (2)
surrogate data in which any nonlinear correlation is removed but the
distribution and linear correlation are preserved, (3) surrogate data in which
large positive and negative returns are replaced with small values, and (4)
surrogate data generated from alternative fat-tailed distributions with the
temporal correlation preserved. We find that all these factors have influence
on the multifractal spectrum. We also find that the temporal structure (linear
or nonlinear) has minor impact on the singularity width of the
multifractal spectrum while the fat tails have major impact on ,
which confirms the earlier results. In addition, the linear correlation is
found to have only a horizontal translation effect on the multifractal spectrum
in which the distance is approximately equal to the difference between its DFA
scaling exponent and 0.5. Our method can also be applied to other financial or
physical variables and other multifractal formalisms.Comment: 6 epl page
Edwards-Wilkinson surface over a spherical substrate: noise in the height fluctuations
We study the steady state fluctuations of an Edwards-Wilkinson type surface
with the substrate taken to be a sphere. We show that the height fluctuations
on circles at a given latitude has the effective action of a perfect Gaussian
noise, just as in the case of fixed radius circles on an infinite planar
substrate. The effective surface tension, which is the overall coefficient of
the action, does not depend on the latitude angle of the circles.Comment: 6 page
Entanglement Entropy in Extended Quantum Systems
After a brief introduction to the concept of entanglement in quantum systems,
I apply these ideas to many-body systems and show that the von Neumann entropy
is an effective way of characterising the entanglement between the degrees of
freedom in different regions of space. Close to a quantum phase transition it
has universal features which serve as a diagnostic of such phenomena. In the
second part I consider the unitary time evolution of such systems following a
`quantum quench' in which a parameter in the hamiltonian is suddenly changed,
and argue that finite regions should effectively thermalise at late times,
after interesting transient effects.Comment: 6 pages. Plenary talk delivered at Statphys 23, Genoa, July 200
Developing an intervention to facilitate family communication about inherited genetic conditions, and training genetic counsellors in its delivery.
Many families experience difficulty in talking about an inherited genetic condition that affects one or more of them. There have now been a number of studies identifying the issues in detail, however few have developed interventions to assist families. The SPRinG collaborative have used the UK Medical Research Council's guidance on Developing and Evaluating Complex Interventions, to work with families and genetic counsellors (GCs) to co-design a psycho-educational intervention to facilitate family communication and promote better coping and adaptation to living with an inherited genetic condition for parents and their children (<18 years). The intervention is modelled on multi-family discussion groups (MFDGs) used in psychiatric settings. The MFDG was developed and tested over three phases. First focus groups with parents, young people, children and health professionals discussed whether MFDG was acceptable and proposed a suitable design. Using evidence and focus group data, the intervention and a training manual were developed and three GCs were trained in its delivery. Finally, a prototype MFDG was led by a family therapist and co-facilitated by the three GCs. Data analysis showed that families attending the focus groups and intervention thought MFDG highly beneficial, and the pilot sessions had a significant impact on their family' functioning. We also demonstrated that it is possible to train GCs to deliver the MFDG intervention. Further studies are now required to test the feasibility of undertaking a definitive randomised controlled trial to evaluate its effectiveness in improving family outcomes before implementing into genetic counselling practice.The National Institute of Health Research funded the study but any views expressed do not necessarily reflect those of the Authority. Funded by NIHR reference number: RP-DG-1211-10015
The use of organic ligands to study the molecular mechanisms of angiogenesis and immunoregulation
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 1999.Includes bibliographical references.by Benjamin E. Turk.Ph.D
Entanglement spectra of critical and near-critical systems in one dimension
The entanglement spectrum of a pure state of a bipartite system is the full
set of eigenvalues of the reduced density matrix obtained from tracing out one
part. Such spectra are known in several cases to contain important information
beyond that in the entanglement entropy. This paper studies the entanglement
spectrum for a variety of critical and near-critical quantum lattice models in
one dimension, chiefly by the iTEBD numerical method, which enables both
integrable and non-integrable models to be studied. We find that the
distribution of eigenvalues in the entanglement spectra agrees with an
approximate result derived by Calabrese and Lefevre to an accuracy of a few
percent for all models studied. This result applies whether the correlation
length is intrinsic or generated by the finite matrix size accessible in iTEBD.
For the transverse Ising model, the known exact results for the entanglement
spectrum are used to confirm the validity of the iTEBD approach. For more
general models, no exact result is available but the iTEBD results directly
test the hypothesis that all moments of the reduced density matrix are
determined by a single parameter.Comment: 6 pages, 5 figure
Exact results for the entanglement across defects in critical chains
We consider fermionic and bosonic quantum chains where a defect separates two
subsystems and compare the corresponding entanglement spectra. With these, we
calculate their R\'enyi entanglement entropies and obtain analytical formulae
for the continuously varying coefficient of the leading logarithmic term. For
the bosonic case we also present numerical results.Comment: 17 pages, 6 figures, some remarks adde
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