6,959 research outputs found
Structure factor of dilute ring polymers
We consider ring polymers in good solvents in the dilute limit. We determine
the structure factor and the monomer-monomer distribution function. We compute
accurately the asymptotic behavior of these functions for small and large
momenta and distances by using field-theoretical methods. Phenomenological
expressions with the correct asymptotic behaviors are also given.Comment: 17 pages, 3 figure
Geometrical optics analysis of the short-time stability properties of the Einstein evolution equations
Many alternative formulations of Einstein's evolution have lately been
examined, in an effort to discover one which yields slow growth of
constraint-violating errors. In this paper, rather than directly search for
well-behaved formulations, we instead develop analytic tools to discover which
formulations are particularly ill-behaved. Specifically, we examine the growth
of approximate (geometric-optics) solutions, studied only in the future domain
of dependence of the initial data slice (e.g. we study transients). By
evaluating the amplification of transients a given formulation will produce, we
may therefore eliminate from consideration the most pathological formulations
(e.g. those with numerically-unacceptable amplification). This technique has
the potential to provide surprisingly tight constraints on the set of
formulations one can safely apply. To illustrate the application of these
techniques to practical examples, we apply our technique to the 2-parameter
family of evolution equations proposed by Kidder, Scheel, and Teukolsky,
focusing in particular on flat space (in Rindler coordinates) and Schwarzchild
(in Painleve-Gullstrand coordinates).Comment: Submitted to Phys. Rev.
Mott transition and dimerization in the one-dimensional SU Hubbard model
The one-dimensional SU Hubbard model is investigated numerically for
, and 5 at half filling and filling using the density-matrix
renormalization-group (DMRG) method. The energy gaps and various quantum
information entropies are calculated. In the half-filled case, finite spin and
charge gaps are found for arbitrary positive if . Furthermore, it is
shown that the transition to the gapped phase at is of
Kosterlitz-Thouless type and is accompanied by a bond dimerization both for
even and odd . In the -filled case, the transition has similar features
as the metal-insulator transition in the half-filled SU(2) Hubbard model. The
charge gap opens exponentially slowly for , the spin sector
remains gapless, and the ground state is non-dimerized.Comment: 9 pages, 12 figure
Spatially nonuniform phases in the one-dimensional SU(n) Hubbard model for commensurate fillings
The one-dimensional repulsive SU Hubbard model is investigated
analytically by bosonization approach and numerically using the density-matrix
renormalization-group (DMRG) method for , and 5 for commensurate
fillings where and are relatively prime. It is shown that the
behavior of the system is drastically different depending on whether ,
, or , the umklapp processes are irrelevant, the model is
equivalent to an -component Luttinger liquid with central charge . When
, the charge and spin modes are decoupled, the umklapp processes open a
charge gap for finite , whereas the spin modes remain gapless and the
central charge . The translational symmetry is not broken in the ground
state for any . On the other hand, when , the charge and spin modes are
coupled, the umklapp processes open gaps in all excitation branches, and a
spatially nonuniform ground state develops. Bond-ordered dimerized, trimerized
or tetramerized phases are found depending on the filling.Comment: 10 pages, 11 figure
Entropy inequalities from reflection positivity
We investigate the question of whether the entropy and the Renyi entropies of
the vacuum state reduced to a region of the space can be represented in terms
of correlators in quantum field theory. In this case, the positivity relations
for the correlators are mapped into inequalities for the entropies. We write
them using a real time version of reflection positivity, which can be
generalized to general quantum systems. Using this generalization we can prove
an infinite sequence of inequalities which are obeyed by the Renyi entropies of
integer index. There is one independent inequality involving any number of
different subsystems. In quantum field theory the inequalities acquire a simple
geometrical form and are consistent with the integer index Renyi entropies
being given by vacuum expectation values of twisting operators in the Euclidean
formulation. Several possible generalizations and specific examples are
analyzed.Comment: Significantly enlarged and corrected version. Counterexamples found
for the most general form of the inequalities. V3: minor change
Zero dimensional area law in a gapless fermion system
The entanglement entropy of a gapless fermion subsystem coupled to a gapless
bulk by a "weak link" is considered. It is demonstrated numerically that each
independent weak link contributes an entropy proportional to lnL, where L is
linear dimension of the subsystem.Comment: 6 pages, 11 figures; added 3d computatio
Exact boundary conditions in numerical relativity using multiple grids: scalar field tests
Cauchy-Characteristic Matching (CCM), the combination of a central 3+1 Cauchy
code with an exterior characteristic code connected across a time-like
interface, is a promising technique for the generation and extraction of
gravitational waves. While it provides a tool for the exact specification of
boundary conditions for the Cauchy evolution, it also allows to follow
gravitational radiation all the way to infinity, where it is unambiguously
defined.
We present a new fourth order accurate finite difference CCM scheme for a
first order reduction of the wave equation around a Schwarzschild black hole in
axisymmetry. The matching at the interface between the Cauchy and the
characteristic regions is done by transfering appropriate characteristic/null
variables. Numerical experiments indicate that the algorithm is fourth order
convergent. As an application we reproduce the expected late-time tail decay
for the scalar field.Comment: 14 pages, 5 figures. Included changes suggested by referee
Evolution of entanglement after a local quench
We study free electrons on an infinite half-filled chain, starting in the
ground state with a bond defect. We find a logarithmic increase of the
entanglement entropy after the defect is removed, followed by a slow relaxation
towards the value of the homogeneous chain. The coefficients depend
continuously on the defect strength.Comment: 14 pages, 9 figures, final versio
Entanglement between particle partitions in itinerant many-particle states
We review `particle partitioning entanglement' for itinerant many-particle
systems. This is defined as the entanglement between two subsets of particles
making up the system. We identify generic features and mechanisms of particle
entanglement that are valid over whole classes of itinerant quantum systems. We
formulate the general structure of particle entanglement in many-fermion ground
states, analogous to the `area law' for the more usually studied entanglement
between spatial regions. Basic properties of particle entanglement are first
elucidated by considering relatively simple itinerant models. We then review
particle-partitioning entanglement in quantum states with more intricate
physics, such as anyonic models and quantum Hall states.Comment: review, about 20 pages. Version 2 has minor revisions
Entanglement entropy of two disjoint intervals in c=1 theories
We study the scaling of the Renyi entanglement entropy of two disjoint blocks
of critical lattice models described by conformal field theories with central
charge c=1. We provide the analytic conformal field theory result for the
second order Renyi entropy for a free boson compactified on an orbifold
describing the scaling limit of the Ashkin-Teller (AT) model on the self-dual
line. We have checked this prediction in cluster Monte Carlo simulations of the
classical two dimensional AT model. We have also performed extensive numerical
simulations of the anisotropic Heisenberg quantum spin-chain with tree-tensor
network techniques that allowed to obtain the reduced density matrices of
disjoint blocks of the spin-chain and to check the correctness of the
predictions for Renyi and entanglement entropies from conformal field theory.
In order to match these predictions, we have extrapolated the numerical results
by properly taking into account the corrections induced by the finite length of
the blocks to the leading scaling behavior.Comment: 37 pages, 23 figure
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