14 research outputs found
Ground state entanglement in quantum spin chains
A microscopic calculation of ground state entanglement for the XY and
Heisenberg models shows the emergence of universal scaling behavior at quantum
phase transitions. Entanglement is thus controlled by conformal symmetry. Away
from the critical point, entanglement gets saturated by a mass scale. Results
borrowed from conformal field theory imply irreversibility of entanglement loss
along renormalization group trajectories. Entanglement does not saturate in
higher dimensions which appears to limit the success of the density matrix
renormalization group technique. A possible connection between majorization and
renormalization group irreversibility emerges from our numerical analysis.Comment: 26 pages, 16 figures, added references, minor changes. Final versio
Fine-grained entanglement loss along renormalization group flows
We explore entanglement loss along renormalization group trajectories as a
basic quantum information property underlying their irreversibility. This
analysis is carried out for the quantum Ising chain as a transverse magnetic
field is changed. We consider the ground-state entanglement between a large
block of spins and the rest of the chain. Entanglement loss is seen to follow
from a rigid reordering, satisfying the majorization relation, of the
eigenvalues of the reduced density matrix for the spin block. More generally,
our results indicate that it may be possible to prove the irreversibility along
RG trajectories from the properties of the vacuum only, without need to study
the whole hamiltonian.Comment: 5 pages, 3 figures; minor change
Entanglement in quantum critical phenomena
Quantum phase transitions occur at zero temperature and involve the
appearance of long-range correlations. These correlations are not due to
thermal fluctuations but to the intricate structure of a strongly entangled
ground state of the system. We present a microscopic computation of the scaling
properties of the ground-state entanglement in several 1D spin chain models
both near and at the quantum critical regimes. We quantify entanglement by
using the entropy of the ground state when the system is traced down to
spins. This entropy is seen to scale logarithmically with , with a
coefficient that corresponds to the central charge associated to the conformal
theory that describes the universal properties of the quantum phase transition.
Thus we show that entanglement, a key concept of quantum information science,
obeys universal scaling laws as dictated by the representations of the
conformal group and its classification motivated by string theory. This
connection unveils a monotonicity law for ground-state entanglement along the
renormalization group flow. We also identify a majorization rule possibly
associated to conformal invariance and apply the present results to interpret
the breakdown of density matrix renormalization group techniques near a
critical point.Comment: 5 pages, 2 figure
Entanglement and alpha entropies for a massive Dirac field in two dimensions
We present some exact results about universal quantities derived from the
local density matrix, for a free massive Dirac field in two dimensions. We
first find the trace of powers of the density matrix in a novel fashion, which
involves the correlators of suitable operators in the sine-Gordon model. These,
in turn, can be written exactly in terms of the solutions of non-linear
differential equations of the Painlev\'e V type. Equipped with the previous
results, we find the leading terms for the entanglement entropy, both for short
and long distances, and showing that in the intermediate regime it can be
expanded in a series of multiple integrals. The previous results have been
checked by direct numerical calculations on the lattice, finding perfect
agreement. Finally, we comment on a possible generalization of the entanglement
entropy c-theorem to the alpha-entropies.Comment: Clarification in section 2, one reference added. 15 pages, 3 figure
Mean Field Approximations and Multipartite Thermal Correlations
The relationship between the mean-field approximations in various interacting
models of statistical physics and measures of classical and quantum
correlations is explored. We present a method that allows us to bound the total
amount of correlations (and hence entanglement) in a physical system in thermal
equilibrium at some temperature in terms of its free energy and internal
energy. This method is first illustrated using two qubits interacting through
the Heisenberg coupling, where entanglement and correlations can be computed
exactly. It is then applied to the one dimensional Ising model in a transverse
magnetic field, for which entanglement and correlations cannot be obtained by
exact methods. We analyze the behavior of correlations in various regimes and
identify critical regions, comparing them with already known results. Finally,
we present a general discussion of the effects of entanglement on the
macroscopic, thermodynamical features of solid-state systems. In particular, we
exploit the fact that a dimensional quantum system in thermal equilibrium
can be made to corresponds to a d+1 classical system in equilibrium to
substitute all entanglement for classical correlations.Comment: 17 pages, 6 figure
Quantum Entanglement in Second-quantized Condensed Matter Systems
The entanglement between occupation-numbers of different single particle
basis states depends on coupling between different single particle basis states
in the second-quantized Hamiltonian. Thus in principle, interaction is not
necessary for occupation-number entanglement to appear. However, in order to
characterize quantum correlation caused by interaction, we use the eigenstates
of the single-particle Hamiltonian as the single particle basis upon which the
occupation-number entanglement is defined. Using the proper single particle
basis, we discuss occupation-number entanglement in important eigenstates,
especially ground states, of systems of many identical particles. The
discussions on Fermi systems start with Fermi gas, Hatree-Fock approximation,
and the electron-hole entanglement in excitations. The entanglement in a
quantum Hall state is quantified as -fln f-(1-f)ln(1-f), where f is the proper
fractional part of the filling factor. For BCS superconductivity, the
entanglement is a function of the relative momentum wavefunction of the Cooper
pair, and is thus directly related to the superconducting energy gap. For a
spinless Bose system, entanglement does not appear in the
Hatree-Gross-Pitaevskii approximation, but becomes important in the Bogoliubov
theory.Comment: 11 pages. Journal versio
Renyi Entropy of the XY Spin Chain
We consider the one-dimensional XY quantum spin chain in a transverse
magnetic field. We are interested in the Renyi entropy of a block of L
neighboring spins at zero temperature on an infinite lattice. The Renyi entropy
is essentially the trace of some power of the density matrix of the
block. We calculate the asymptotic for analytically in terms of
Klein's elliptic - function. We study the limiting entropy as a
function of its parameter . We show that up to the trivial addition
terms and multiplicative factors, and after a proper re-scaling, the Renyi
entropy is an automorphic function with respect to a certain subgroup of the
modular group; moreover, the subgroup depends on whether the magnetic field is
above or below its critical value. Using this fact, we derive the
transformation properties of the Renyi entropy under the map and show that the entropy becomes an elementary function of the
magnetic field and the anisotropy when is a integer power of 2, this
includes the purity . We also analyze the behavior of the entropy as
and and at the critical magnetic field and in the
isotropic limit [XX model].Comment: 28 Pages, 1 Figur
Choice of the initial antiretroviral treatment for HIV-positive individuals in the era of integrase inhibitors
BACKGROUND: We aimed to describe the most frequently prescribed initial antiretroviral therapy (ART) regimens in recent years in HIV-positive persons in the Cohort of the Spanish HIV/AIDS Research Network (CoRIS) and to investigate factors associated with the choice of each regimen. METHODS: We analyzed initial ART regimens prescribed in adults participating in CoRIS from 2014 to 2017. Only regimens prescribed in >5% of patients were considered. We used multivariable multinomial regression to estimate Relative Risk Ratios (RRRs) for the association between sociodemographic and clinical characteristics and the choice of the initial regimen. RESULTS: Among 2874 participants, abacavir(ABC)/lamivudine(3TC)/dolutegavir(DTG) was the most frequently prescribed regimen (32.1%), followed by tenofovir disoproxil fumarate (TDF)/emtricitabine (FTC)/elvitegravir(EVG)/cobicistat(COBI) (14.9%), TDF/FTC/rilpivirine (RPV) (14.0%), tenofovir alafenamide (TAF)/FTC/EVG/COBI (13.7%), TDF/FTC+DTG (10.0%), TDF/FTC+darunavir/ritonavir or darunavir/cobicistat (bDRV) (9.8%) and TDF/FTC+raltegravir (RAL) (5.6%). Compared with ABC/3TC/DTG, starting TDF/FTC/RPV was less likely in patients with CD4100.000 copies/mL. TDF/FTC+DTG was more frequent in those with CD4100.000 copies/mL. TDF/FTC+RAL and TDF/FTC+bDRV were also more frequent among patients with CD4<200 cells//muL and with transmission categories other than men who have sex with men. Compared with ABC/3TC/DTG, the prescription of other initial ART regimens decreased from 2014-2015 to 2016-2017 with the exception of TDF/FTC+DTG. Differences in the choice of the initial ART regimen were observed by hospitals' location. CONCLUSIONS: The choice of initial ART regimens is consistent with Spanish guidelines' recommendations, but is also clearly influenced by physician's perception based on patient's clinical and sociodemographic variables and by the prescribing hospital location
A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)
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Evolution of entanglement entropy in one-dimensional systems
We study the unitary time evolution of the entropy of entanglement of a one-dimensional system between the degrees of freedom in an interval of length l and its complement, starting from a pure state which is not an eigenstate of the Hamiltonian. We use path integral methods of quantum field theory as well as explicit computations for the transverse Ising spin chain. In both cases, there is a maximum speed v of propagation of signals. In general the entanglement entropy increases linearly with time t up to t = l/2v, after which it saturates at a value proportional to l, the coefficient depending on the initial state. This behaviour may be understood as a consequence of causality