26,032 research outputs found
Entanglement in quantum critical phenomena
Quantum phase transitions occur at zero temperature and involve the
appearance of long-range correlations. These correlations are not due to
thermal fluctuations but to the intricate structure of a strongly entangled
ground state of the system. We present a microscopic computation of the scaling
properties of the ground-state entanglement in several 1D spin chain models
both near and at the quantum critical regimes. We quantify entanglement by
using the entropy of the ground state when the system is traced down to
spins. This entropy is seen to scale logarithmically with , with a
coefficient that corresponds to the central charge associated to the conformal
theory that describes the universal properties of the quantum phase transition.
Thus we show that entanglement, a key concept of quantum information science,
obeys universal scaling laws as dictated by the representations of the
conformal group and its classification motivated by string theory. This
connection unveils a monotonicity law for ground-state entanglement along the
renormalization group flow. We also identify a majorization rule possibly
associated to conformal invariance and apply the present results to interpret
the breakdown of density matrix renormalization group techniques near a
critical point.Comment: 5 pages, 2 figure
Critical phenomena in Newtonian gravity
We investigate the stability of self-similar solutions for a gravitationally
collapsing isothermal sphere in Newtonian gravity by means of a normal mode
analysis. It is found that the Hunter series of solutions are highly unstable,
while neither the Larson-Penston solution nor the homogeneous collapse one have
an analytic unstable mode. Since the homogeneous collapse solution is known to
suffer the kink instability, the present result and recent numerical
simulations strongly support a proposition that the Larson-Penston solution
will be realized in astrophysical situations. It is also found that the Hunter
(A) solution has a single unstable mode, which implies that it is a critical
solution associated with some critical phenomena which are analogous to those
in general relativity. The critical exponent is calculated as
. In contrast to the general relativistic case, the order
parameter will be the collapsed mass. In order to obtain a complete picture of
the Newtonian critical phenomena, full numerical simulations will be needed.Comment: 25 pages, 7 figures, accepted for publication in Physical Review
Critical phenomena in complex networks
The combination of the compactness of networks, featuring small diameters,
and their complex architectures results in a variety of critical effects
dramatically different from those in cooperative systems on lattices. In the
last few years, researchers have made important steps toward understanding the
qualitatively new critical phenomena in complex networks. We review the
results, concepts, and methods of this rapidly developing field. Here we mostly
consider two closely related classes of these critical phenomena, namely
structural phase transitions in the network architectures and transitions in
cooperative models on networks as substrates. We also discuss systems where a
network and interacting agents on it influence each other. We overview a wide
range of critical phenomena in equilibrium and growing networks including the
birth of the giant connected component, percolation, k-core percolation,
phenomena near epidemic thresholds, condensation transitions, critical
phenomena in spin models placed on networks, synchronization, and
self-organized criticality effects in interacting systems on networks. We also
discuss strong finite size effects in these systems and highlight open problems
and perspectives.Comment: Review article, 79 pages, 43 figures, 1 table, 508 references,
extende
Critical Phenomena Inside Global Monopoles
The gravitational collapse of a triplet scalar field is examined assuming a
hedgehog ansatz for the scalar field. Whereas the seminal work by Choptuik with
a single, strictly spherically symmetric scalar field found a discretely
self-similar (DSS) solution at criticality with echoing period ,
here a new DSS solution is found with period . This new critical
solution is also observed in the presence of a symmetry breaking potential as
well as within a global monopole. The triplet scalar field model contains
Choptuik's original model in a certain region of parameter space, and hence his
original DSS solution is also a solution. However, the choice of a hedgehog
ansatz appears to exclude the original DSS.Comment: 5 pages, 5 figure
Entanglement and boundary critical phenomena
We investigate boundary critical phenomena from a quantum information
perspective. Bipartite entanglement in the ground state of one-dimensional
quantum systems is quantified using the Renyi entropy S_alpha, which includes
the von Neumann entropy (alpha=1) and the single-copy entanglement
(alpha=infinity) as special cases. We identify the contribution from the
boundary entropy to the Renyi entropy, and show that there is an entanglement
loss along boundary renormalization group (RG) flows. This property, which is
intimately related to the Affleck-Ludwig g-theorem, can be regarded as a
consequence of majorization relations between the spectra of the reduced
density matrix along the boundary RG flows. We also point out that the bulk
contribution to the single-copy entanglement is half of that to the von Neumann
entropy, whereas the boundary contribution is the same.Comment: 4 pages, 2 figure
Critical phenomena in exponential random graphs
The exponential family of random graphs is one of the most promising class of
network models. Dependence between the random edges is defined through certain
finite subgraphs, analogous to the use of potential energy to provide
dependence between particle states in a grand canonical ensemble of statistical
physics. By adjusting the specific values of these subgraph densities, one can
analyze the influence of various local features on the global structure of the
network. Loosely put, a phase transition occurs when a singularity arises in
the limiting free energy density, as it is the generating function for the
limiting expectations of all thermodynamic observables. We derive the full
phase diagram for a large family of 3-parameter exponential random graph models
with attraction and show that they all consist of a first order surface phase
transition bordered by a second order critical curve.Comment: 14 pages, 8 figure
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