2,250 research outputs found
Entanglement and Quantum Phase Transition Revisited
We show that, for an exactly solvable quantum spin model, a discontinuity in
the first derivative of the ground state concurrence appears in the absence of
quantum phase transition. It is opposed to the popular belief that the
non-analyticity property of entanglement (ground state concurrence) can be used
to determine quantum phase transitions. We further point out that the
analyticity property of the ground state concurrence in general can be more
intricate than that of the ground state energy. Thus there is no one-to-one
correspondence between quantum phase transitions and the non-analyticity
property of the concurrence. Moreover, we show that the von Neumann entropy, as
another measure of entanglement, can not reveal quantum phase transition in the
present model. Therefore, in order to link with quantum phase transitions, some
other measures of entanglement are needed.Comment: RevTeX 4, 4 pages, 1 EPS figures. some modifications in the text.
Submitted to Phys. Rev.
Universality in the entanglement structure of ferromagnets
Systems of exchange-coupled spins are commonly used to model ferromagnets.
The quantum correlations in such magnets are studied using tools from quantum
information theory. Isotropic ferromagnets are shown to possess a universal
low-temperature density matrix which precludes entanglement between spins, and
the mechanism of entanglement cancellation is investigated, revealing a core of
states resistant to pairwise entanglement cancellation. Numerical studies of
one-, two-, and three-dimensional lattices as well as irregular geometries
showed no entanglement in ferromagnets at any temperature or magnetic field
strength.Comment: 4 pages, 2 figure
Scaling of entanglement between separated blocks in spin chains at criticality
We compute the entanglement between separated blocks in certain spin models
showing that at criticality this entanglement is a function of the ratio of the
separation to the length of the blocks and can be written as a product of a
power law and an exponential decay. It thereby interpolates between the
entanglement of individual spins and blocks of spins. It captures features of
correlation functions at criticality as well as the monogamous nature of
entanglement. We exemplify invariant features of this entanglement to
microscopic changes within the same universality class. We find this
entanglement to be invariant with respect to simultaneous scale transformations
of the separation and the length of the blocks. As a corollary, this study
estimates the entanglement between separated regions of those quantum fields to
which the considered spin models map at criticality.Comment: 4 pages, 3 figures; comments welcom
Violation of the entropic area law for Fermions
We investigate the scaling of the entanglement entropy in an infinite
translational invariant Fermionic system of any spatial dimension. The states
under consideration are ground states and excitations of tight-binding
Hamiltonians with arbitrary interactions. We show that the entropy of a finite
region typically scales with the area of the surface times a logarithmic
correction. Thus, in contrast to analogous Bosonic systems, the entropic area
law is violated for Fermions. The relation between the entanglement entropy and
the structure of the Fermi surface is discussed, and it is proven, that the
presented scaling law holds whenever the Fermi surface is finite. This is in
particular true for all ground states of Hamiltonians with finite range
interactions.Comment: 5 pages, 1 figur
Area law and vacuum reordering in harmonic networks
We review a number of ideas related to area law scaling of the geometric
entropy from the point of view of condensed matter, quantum field theory and
quantum information. An explicit computation in arbitrary dimensions of the
geometric entropy of the ground state of a discretized scalar free field theory
shows the expected area law result. In this case, area law scaling is a
manifestation of a deeper reordering of the vacuum produced by majorization
relations. Furthermore, the explicit control on all the eigenvalues of the
reduced density matrix allows for a verification of entropy loss along the
renormalization group trajectory driven by the mass term. A further result of
our computation shows that single-copy entanglement also obeys area law
scaling, majorization relations and decreases along renormalization group
flows.Comment: 15 pages, 6 figures; typos correcte
Configuration-Space Location of the Entanglement between Two Subsystems
In this paper we address the question: where in configuration space is the
entanglement between two particles located? We present a thought-experiment,
equally applicable to discrete or continuous-variable systems, in which one or
both parties makes a preliminary measurement of the state with only enough
resolution to determine whether or not the particle resides in a chosen region,
before attempting to make use of the entanglement. We argue that this provides
an operational answer to the question of how much entanglement was originally
located within the chosen region. We illustrate the approach in a spin system,
and also in a pair of coupled harmonic oscillators. Our approach is
particularly simple to implement for pure states, since in this case the
sub-ensemble in which the system is definitely located in the restricted region
after the measurement is also pure, and hence its entanglement can be simply
characterised by the entropy of the reduced density operators. For our spin
example we present results showing how the entanglement varies as a function of
the parameters of the initial state; for the continuous case, we find also how
it depends on the location and size of the chosen regions. Hence we show that
the distribution of entanglement is very different from the distribution of the
classical correlations.Comment: RevTex, 12 pages, 9 figures (28 files). Modifications in response to
journal referee
GHZ extraction yield for multipartite stabilizer states
Let be an arbitrary stabilizer state distributed between three
remote parties, such that each party holds several qubits. Let be a
stabilizer group of . We show that can be converted by local
unitaries into a collection of singlets, GHZ states, and local one-qubit
states. The numbers of singlets and GHZs are determined by dimensions of
certain subgroups of . For an arbitrary number of parties we find a
formula for the maximal number of -partite GHZ states that can be extracted
from by local unitaries. A connection with earlier introduced measures
of multipartite correlations is made. An example of an undecomposable
four-party stabilizer state with more than one qubit per party is given. These
results are derived from a general theoretical framework that allows one to
study interconversion of multipartite stabilizer states by local Clifford group
operators. As a simple application, we study three-party entanglement in
two-dimensional lattice models that can be exactly solved by the stabilizer
formalism.Comment: 12 pages, 1 figur
Mixed-state fidelity and quantum criticality at finite temperature
We extend to finite temperature the fidelity approach to quantum phase
transitions (QPTs). This is done by resorting to the notion of mixed-state
fidelity that allows one to compare two density matrices corresponding to two
different thermal states. By exploiting the same concept we also propose a
finite-temperature generalization of the Loschmidt echo. Explicit analytical
expressions of these quantities are given for a class of quasi-free fermionic
Hamiltonians. A numerical analysis is performed as well showing that the
associated QPTs show their signatures in a finite range of temperatures.Comment: 7 pages, 4 figure
Optimal minimal measurements of mixed states
The optimal and minimal measuring strategy is obtained for a two-state system
prepared in a mixed state with a probability given by any isotropic a priori
distribution. We explicitly construct the specific optimal and minimal
generalized measurements, which turn out to be independent of the a priori
probability distribution, obtaining the best guesses for the unknown state as
well as a closed expression for the maximal mean averaged fidelity. We do this
for up to three copies of the unknown state in a way which leads to the
generalization to any number of copies, which we then present and prove.Comment: 20 pages, no figure
Entanglement and Quantum Phases in the Anisotropic Ferromagnetic Heisenberg Chain in the Presence of Domain Walls
We discuss entanglement in the spin-1/2 anisotropic ferromagnetic Heisenberg
chain in the presence of a boundary magnetic field generating domain walls. By
increasing the magnetic field, the model undergoes a first-order quantum phase
transition from a ferromagnetic to a kink-type phase, which is associated to a
jump in the content of entanglement available in the system. Above the critical
point, pairwise entanglement is shown to be non-vanishing and independent of
the boundary magnetic field for large chains. Based on this result, we provide
an analytical expression for the entanglement between arbitrary spins. Moreover
the effects of the quantum domains on the gapless region and for
antiferromagnetic anisotropy are numerically analysed. Finally multiparticle
entanglement properties are considered, from which we establish a
characterization of the critical anisotropy separating the gapless regime from
the kink-type phase.Comment: v3: 7 pages, including 4 figures and 1 table. Published version. v2:
One section (V) added and references update
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