745 research outputs found
Phase diagram of the SO(n) bilinear-biquadratic chain from many-body entanglement
Here we investigate the phase diagram of the SO(n) bilinear-biquadratic
quantum spin chain by studying the global quantum correlations of the ground
state. We consider the cases of n=3,4 and 5 and focus on the geometric
entanglement in the thermodynamic limit. Apart from capturing all the known
phase transitions, our analysis shows a number of novel distinctive behaviors
in the phase diagrams which we conjecture to be general and valid for arbitrary
n. In particular, we provide an intuitive argument in favor of an infinite
entanglement length in the system at a purely-biquadratic point. Our results
are also compared to other methods, such as fidelity diagrams.Comment: 7 pages, 4 figures. Revised version. To appear in PR
Entanglement and SU(n) symmetry in one-dimensional valence bond solid states
Here we evaluate the many-body entanglement properties of a generalized SU(n)
valence bond solid state on a chain. Our results follow from a derivation of
the transfer matrix of the system which, in combination with symmetry
properties, allows for a new, elegant and straightforward evaluation of
different entanglement measures. In particular, the geometric entanglement per
block, correlation length, von Neumann and R\'enyi entropies of a block,
localizable entanglement and entanglement length are obtained in a very simple
way. All our results are in agreement with previous derivations for the SU(2)
case.Comment: 4 pages, 2 figure
Visualizing elusive phase transitions with geometric entanglement
We show that by examining the global geometric entanglement it is possible to
identify "elusive" or hard to detect quantum phase transitions. We analyze
several one-dimensional quantum spin chains and demonstrate the existence of
non-analyticities in the geometric entanglement, in particular across a
Kosterlitz-Thouless transition and across a transition for a gapped deformed
Affleck-Kennedy-Lieb-Tasaki chain. The observed non-analyticities can be
understood and classified in connection to the nature of the transitions, and
are in sharp contrast to the analytic behavior of all the two-body reduced
density operators and their derived entanglement measures.Comment: 7 pages, 5 figures, revised version, accepted for publication in PR
Weakly-entangled states are dense and robust
Motivated by the mathematical definition of entanglement we undertake a
rigorous analysis of the separability and non-distillability properties in the
neighborhood of those three-qubit mixed states which are entangled and
completely bi-separable. Our results are not only restricted to this class of
quantum states, since they rest upon very general properties of mixed states
and Unextendible Product Bases for any possible number of parties. Robustness
against noise of the relevant properties of these states implies the
significance of their possible experimental realization, therefore being of
physical -and not exclusively mathematical- interest.Comment: 4 pages, final version, accepted for publication in PR
Numerical study of the hard-core Bose-Hubbard Model on an Infinite Square Lattice
We present a study of the hard-core Bose-Hubbard model at zero temperature on
an infinite square lattice using the infinite Projected Entangled Pair State
algorithm [Jordan et al., Phys. Rev. Lett. 101, 250602 (2008)]. Throughout the
whole phase diagram our values for the ground state energy, particle density
and condensate fraction accurately reproduce those previously obtained by other
methods. We also explore ground state entanglement, compute two-point
correlators and conduct a fidelity-based analysis of the phase diagram.
Furthermore, for illustrative purposes we simulate the response of the system
when a perturbation is suddenly added to the Hamiltonian.Comment: 8 pages, 6 figure
Como enseñar la división en la Escuela Primaria. Un ejemplo de utilización de los recursos del CRDM-GB para la investigación y la formación del profesorado.
Comunicación presentada en: XVI Simposio de la Sociedad Española de Investigación en Educación Matemática (SEIEM). 20-22 Septiembre, 2012. Universidad Internacional de Andalucía en Baeza (Jaén).Comunicaremos aspectos de un trabajo colectivo realizado en un taller donde un
equipo de seis docentes de diferentes niveles y modalidades, se propuso estudiar,
problematizar y reconstruir un informe de actividades para la enseñanza de la división
en el nivel primario. Ese informe surgió de un trabajo en colaboración publicado en
1985 por la Universidad de Bordeaux, y se implementó reiteradamente en la Escuela
Jules Michelet de Talence. En este establecimiento público, durante más de 25 años, se
confrontaron con la contingencia, estudios teóricos en el marco de la Teoría de las
Situaciones Didácticas. El taller se desarrolló sistemáticamente durante el año 2011
siendo su objetivo: “estudiar la secuencia para enseñar la división, y profundizar en el
texto para acordar sobre el modo de comunicación de dicha secuencia”. El acceso a los
recursos documentales disponibles en la Universidad Jaime I (España), suministra
valiosos aportes para la reconstrucción de la secuencia y posibles modos de
comunicación a otros actores del sistema.Communicate aspects of a collective work done in a workshop where a team of
six teachers from different levels and modalities set out to study, problematize and
reconstruct an activity report for the division teaching at the primary level. This report
grew out of a collaborative work published in 1985 by the University of Bordeaux, and
consistently implemented in the School of Talence Jules Michelet. In this public
establishment for over 25 years, are confronted with the contingency theoretical studies
in the framework of the theory of Didactic Situations. The workshop was developed
systematically in 2011 and aims to "study the sequence to teach the division, and further
in the text to agree on the mode of communication of that sequence.". Access to
documentary resources available at the University Jaume I (Spain), provides valuable
input for the reconstruction of the sequence and possible modes of communication to
other actors in the system
Universality of Entanglement and Quantum Computation Complexity
We study the universality of scaling of entanglement in Shor's factoring
algorithm and in adiabatic quantum algorithms across a quantum phase transition
for both the NP-complete Exact Cover problem as well as the Grover's problem.
The analytic result for Shor's algorithm shows a linear scaling of the entropy
in terms of the number of qubits, therefore difficulting the possibility of an
efficient classical simulation protocol. A similar result is obtained
numerically for the quantum adiabatic evolution Exact Cover algorithm, which
also shows universality of the quantum phase transition the system evolves
nearby. On the other hand, entanglement in Grover's adiabatic algorithm remains
a bounded quantity even at the critical point. A classification of scaling of
entanglement appears as a natural grading of the computational complexity of
simulating quantum phase transitions.Comment: 30 pages, 17 figures, accepted for publication in PR
Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
We explain how to implement, in the context of projected entangled-pair
states (PEPS), the general procedure of fermionization of a tensor network
introduced in [P. Corboz, G. Vidal, Phys. Rev. B 80, 165129 (2009)]. The
resulting fermionic PEPS, similar to previous proposals, can be used to study
the ground state of interacting fermions on a two-dimensional lattice. As in
the bosonic case, the cost of simulations depends on the amount of entanglement
in the ground state and not directly on the strength of interactions. The
present formulation of fermionic PEPS leads to a straightforward numerical
implementation that allowed us to recycle much of the code for bosonic PEPS. We
demonstrate that fermionic PEPS are a useful variational ansatz for interacting
fermion systems by computing approximations to the ground state of several
models on an infinite lattice. For a model of interacting spinless fermions,
ground state energies lower than Hartree-Fock results are obtained, shifting
the boundary between the metal and charge-density wave phases. For the t-J
model, energies comparable with those of a specialized Gutzwiller-projected
ansatz are also obtained.Comment: 25 pages, 35 figures (revised version
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