7,892 research outputs found
Entanglement entropy and quantum field theory: a non-technical introduction
In these proceedings we give a pedagogical and non-technical introduction to
the Quantum Field Theory approach to entanglement entropy. Particular attention
is devoted to the one space dimensional case, with a linear dispersion
relation, that, at a quantum critical point, can be effectively described by a
two-dimensional Conformal Field Theory.Comment: 10 Pages, 2 figures. Talk given at the conference "Entanglement in
Physical and information sciences", Centro Ennio de Giorgi, Pisa, December
200
On entanglement evolution across defects in critical chains
We consider a local quench where two free-fermion half-chains are coupled via
a defect. We show that the logarithmic increase of the entanglement entropy is
governed by the same effective central charge which appears in the ground-state
properties and which is known exactly. For unequal initial filling of the
half-chains, we determine the linear increase of the entanglement entropy.Comment: 11 pages, 5 figures, minor changes, reference adde
Corrections to scaling in entanglement entropy from boundary perturbations
We investigate the corrections to scaling of the Renyi entropies of a region
of size l at the end of a semi-infinite one-dimensional system described by a
conformal field theory when the corrections come from irrelevant boundary
operators. The corrections from irrelevant bulk operators with scaling
dimension x have been studied by Cardy and Calabrese (2010), and they found not
only the expected corrections of the form l^(4-2x) but also unusual corrections
that could not have been anticipated by finite-size scaling arguments alone.
However, for the case of perturbations from irrelevant boundary operators we
find that the only corrections that can occur to leading order are of the form
l^(2-2x_b) for boundary operators with scaling dimension x_b < 3/2, and l^(-1)
when x_b > 3/2. When x_b=3/2 they are of the form l^(-1)log(l). A marginally
irrelevant boundary perturbation will give leading corrections going as
log(l)^(-3). No unusual corrections occur when perturbing with a boundary
operator.Comment: 8 pages. Minor improvements and updated references. Published versio
Entropy in quantum chromodynamics
We review the role of zero-temperature entropy in several closely-related
contexts in QCD. The first is entropy associated with disordered condensates,
including . The second is vacuum entropy arising from QCD
solitons such as center vortices, yielding confinement and chiral symmetry
breaking. The third is entanglement entropy, which is entropy associated with a
pure state, such as the QCD vacuum, when the state is partially unobserved and
unknown. Typically, entanglement entropy of an unobserved three-volume scales
not with the volume but with the area of its bounding surface. The fourth
manifestation of entropy in QCD is the configurational entropy of
light-particle world-lines and flux tubes; we argue that this entropy is
critical for understanding how confinement produces chiral symmetry breakdown,
as manifested by a dynamically-massive quark, a massless pion, and a condensate.Comment: 22 pages, 2 figures. Preprint version of invited review for Modern
Physics Letters
Concurrence in collective models
We review the entanglement properties in collective models and their
relationship with quantum phase transitions. Focusing on the concurrence which
characterizes the two-spin entanglement, we show that for first-order
transition, this quantity is singular but continuous at the transition point,
contrary to the common belief. We also propose a conjecture for the concurrence
of arbitrary symmetric states which connects it with a recently proposed
criterion for bipartite entanglement.Comment: 8 pages, 2 figures, published versio
Entanglement of excited states in critical spin chians
Renyi and von Neumann entropies quantifying the amount of entanglement in
ground states of critical spin chains are known to satisfy a universal law
which is given by the Conformal Field Theory (CFT) describing their scaling
regime. This law can be generalized to excitations described by primary fields
in CFT, as was done in reference (Alcaraz et. al., Phys. Rev. Lett. 106, 201601
(2011)), of which this work is a completion. An alternative derivation is
presented, together with numerical verifications of our results in different
models belonging to the c=1,1/2 universality classes. Oscillations of the Renyi
entropy in excited states and descendant fields are also discussed.Comment: 23 pages, 13 figure
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
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
Fluctuations in subsystems of the zero temperature XX chain: Emergence of an effective temperature
The zero-temperature XX chain is studied with emphasis on the properties of a
block of spins inside the chain. We investigate the quantum fluctuations
resulting from the entanglement of the block with the rest of the chain using
analytical as well as numerical (density matrix renormalization group) methods.
It is found that the rest of the chain acts as a thermal environment and an
effective temperature can be introduced to describe the fluctuations. We show
that the effective temperature description is robust in the sense that several
independent definitions (through fluctuation dissipation theorem, comparing
with a finite temperature system) yield the same functional form in the limit
of large block size (). The effective temperature can also be shown
to satisfy the basic requirements on how it changes when two bodies of equal or
unequal temperatures are brought into contact.Comment: 19 pages, 7 figure
Quantum Quench from a Thermal Initial State
We consider a quantum quench in a system of free bosons, starting from a
thermal initial state. As in the case where the system is initially in the
ground state, any finite subsystem eventually reaches a stationary thermal
state with a momentum-dependent effective temperature. We find that this can,
in some cases, even be lower than the initial temperature. We also study
lattice effects and discuss more general types of quenches.Comment: 6 pages, 2 figures; short published version, added references, minor
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