2,917 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
Time-optimal Hamiltonian simulation and gate synthesis using homogeneous local unitaries
Motivated by experimental limitations commonly met in the design of solid
state quantum computers, we study the problems of non-local Hamiltonian
simulation and non-local gate synthesis when only homogeneous local unitaries
are performed in order to tailor the available interaction. Homogeneous (i.e.
identical for all subsystems) local manipulation implies a more refined
classification of interaction Hamiltonians than the inhomogeneous case, as well
as the loss of universality in Hamiltonian simulation. For the case of
symmetric two-qubit interactions, we provide time-optimal protocols for both
Hamiltonian simulation and gate synthesis.Comment: 7 page
Entanglement renormalization in fermionic systems
We demonstrate, in the context of quadratic fermion lattice models in one and
two spatial dimensions, the potential of entanglement renormalization (ER) to
define a proper real-space renormalization group transformation. Our results
show, for the first time, the validity of the multi-scale entanglement
renormalization ansatz (MERA) to describe ground states in two dimensions, even
at a quantum critical point. They also unveil a connection between the
performance of ER and the logarithmic violations of the boundary law for
entanglement in systems with a one-dimensional Fermi surface. ER is recast in
the language of creation/annihilation operators and correlation matrices.Comment: 5 pages, 4 figures Second appendix adde
Violation of area-law scaling for the entanglement entropy in spin 1/2 chains
Entanglement entropy obeys area law scaling for typical physical quantum
systems. This may naively be argued to follow from locality of interactions. We
show that this is not the case by constructing an explicit simple spin chain
Hamiltonian with nearest neighbor interactions that presents an entanglement
volume scaling law. This non-translational model is contrived to have couplings
that force the accumulation of singlet bonds across the half chain. Our result
is complementary to the known relation between non-translational invariant,
nearest neighbor interacting Hamiltonians and QMA complete problems.Comment: 9 pages, 4 figure
Felipe II y el constitucionalismo aragonés
Los hechos ocurridos en Aragón entre 1590 y 1591 generaron una importante literatura histórica en los años siguientes. Gregorio Colás intenta reconstruir los principales puntos argumentativos. Algunas de las obras respondieron a un clima de presión y censura que condicionó en ocasiones una cierta visión apologética de la figura de Felipe II y que obligó a esconder muchos de los verdaderos sentimientos que promovió el final del constitucionalismo aragonés.Els esdeveniments que van tenir lloc a Aragó entre 1590 i 1591 generaren una important literatura historica als anys següents. Gregorio Colás intenta reconstruir els principals punts de I'argumentació. Algunes de les obres respongueren a un clima de pressió i censura que va condicionar, de vegades, una certa visió apologktica de la figura de Felip II, i que va forcar a que s'amaguessin molts dels veritables sentiments promoguts per la fi del constitucionalisme aragonès.Events which took place between 1590 and 1591 in Aragon gave birth to an important historical literature during the following years. Gregorio Colás tries here to reconstruct its main explanatory grounds. Some of the litarary pieces responded to an atmosphere of censorship and coercion ,which yielded eventually a certain apologetic vision about Philip II, and forced to conceal many of the true feeling generated by the end of the Aragonese constitucionalism
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
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
Entangling power of permutation invariant quantum states
We investigate the von Neumann entanglement entropy as function of the size
of a subsystem for permutation invariant ground states in models with finite
number of states per site, e.g., in quantum spin models. We demonstrate that
the entanglement entropy of sites in a system of length generically
grows as , where is the on-site spin
and is a function depending only on magnetization.Comment: 6 pages, 2 figure
Momentum-space analysis of multipartite entanglement at quantum phase transitions
We investigate entanglement properties at quantum phase transitions of an
integrable extended Hubbard model in the momentum space representation. Two
elementary subsystems are recognized: the single mode of an electron, and the
pair of modes (electrons coupled through the eta-pairing mechanism). We first
detect the two/multi-partite nature of each quantum phase transition by a
comparative study of the singularities of Von Neumann entropy and quantum
mutual information. We establish the existing relations between the
correlations in the momentum representation and those exhibited in the
complementary picture: the direct lattice representation. The presence of
multipartite entanglement is then investigated in detail through the Q-measure,
namely a generalization of the Meyer-Wallach measure of entanglement. Such a
measure becomes increasingly sensitive to correlations of a multipartite nature
increasing the size of the reduced density matrix. In momentum space, we
succeed in obtaining the latter for our system at arbitrary size and we relate
its behaviour to the nature of the various QPTs.Comment: 8 pages, 4 figure
Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
This work explores the use of a tree tensor network ansatz to simulate the
ground state of a local Hamiltonian on a two-dimensional lattice. By exploiting
the entropic area law, the tree tensor network ansatz seems to produce
quasi-exact results in systems with sizes well beyond the reach of exact
diagonalisation techniques. We describe an algorithm to approximate the ground
state of a local Hamiltonian on a L times L lattice with the topology of a
torus. Accurate results are obtained for L={4,6,8}, whereas approximate results
are obtained for larger lattices. As an application of the approach, we analyse
the scaling of the ground state entanglement entropy at the quantum critical
point of the model. We confirm the presence of a positive additive constant to
the area law for half a torus. We also find a logarithmic additive correction
to the entropic area law for a square block. The single copy entanglement for
half a torus reveals similar corrections to the area law with a further term
proportional to 1/L.Comment: Major rewrite, new version published in Phys. Rev. B with highly
improved numerical results for the scaling of the entropies and several new
sections. The manuscript has now 19 pages and 30 Figure
- …