2,422 research outputs found
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
Superballistic Diffusion of Entanglement in Disordered Spin Chains
We study the dynamics of a single excitation in an infinite XXZ spin chain,
which is launched from the origin. We study the time evolution of the spread of
entanglement in the spin chain and obtain an expression for the second order
spatial moment of concurrence, about the origin, for both ordered and
disordered chains. In this way, we show that a finite central disordered region
can lead to sustained superballistic growth in the second order spatial moment
of entanglement within the chain.Comment: 5 pages, 1 figur
The Hidden Spatial Geometry of Non-Abelian Gauge Theories
The Gauss law constraint in the Hamiltonian form of the gauge theory
of gluons is satisfied by any functional of the gauge invariant tensor variable
. Arguments are given that the tensor is a more appropriate variable. When the Hamiltonian
is expressed in terms of or , the quantity appears.
The gauge field Bianchi and Ricci identities yield a set of partial
differential equations for in terms of . One can show that
is a metric-compatible connection for with torsion, and that the curvature
tensor of is that of an Einstein space. A curious 3-dimensional
spatial geometry thus underlies the gauge-invariant configuration space of the
theory, although the Hamiltonian is not invariant under spatial coordinate
transformations. Spatial derivative terms in the energy density are singular
when . These singularities are the analogue of the centrifugal
barrier of quantum mechanics, and physical wave-functionals are forced to
vanish in a certain manner near . It is argued that such barriers are
an inevitable result of the projection on the gauge-invariant subspace of the
Hilbert space, and that the barriers are a conspicuous way in which non-abelian
gauge theories differ from scalar field theories.Comment: 19 pages, TeX, CTP #223
Renormalization group transformations on quantum states
We construct a general renormalization group transformation on quantum
states, independent of any Hamiltonian dynamics of the system. We illustrate
this procedure for translational invariant matrix product states in one
dimension and show that product, GHZ, W and domain wall states are special
cases of an emerging classification of the fixed points of this
coarse--graining transformation.Comment: 5 pages, 2 figur
Parity effects in the scaling of block entanglement in gapless spin chains
We consider the Renyi alpha-entropies for Luttinger liquids (LL). For large
block lengths l these are known to grow like ln l. We show that there are
subleading terms that oscillate with frequency 2k_F (the Fermi wave number of
the LL) and exhibit a universal power-law decay with l. The new critical
exponent is equal to K/(2 alpha), where K is the LL parameter. We present
numerical results for the anisotropic XXZ model and the full analytic solution
for the free fermion (XX) point.Comment: 4 pages, 5 figures. Final version accepted in PR
Density of defects and the scaling law of the entanglement entropy in quantum phase transition of one dimensional spin systems induced by a quench
We have studied quantum phase transition induced by a quench in different one
dimensional spin systems. Our analysis is based on the dynamical mechanism
which envisages nonadiabaticity in the vicinity of the critical point. This
causes spin fluctuation which leads to the random fluctuation of the Berry
phase factor acquired by a spin state when the ground state of the system
evolves in a closed path. The two-point correlation of this phase factor is
associated with the probability of the formation of defects. In this framework,
we have estimated the density of defects produced in several one dimensional
spin chains. At the critical region, the entanglement entropy of a block of
spins with the rest of the system is also estimated which is found to increase
logarithmically with . The dependence on the quench time puts a constraint
on the block size . It is also pointed out that the Lipkin-Meshkov-Glick
model in point-splitting regularized form appears as a combination of the XXX
model and Ising model with magnetic field in the negative z-axis. This unveils
the underlying conformal symmetry at criticality which is lost in the sharp
point limit. Our analysis shows that the density of defects as well as the
scaling behavior of the entanglement entropy follows a universal behavior in
all these systems.Comment: 4 figures, Accepted in Phys. Rev.
A mechanobiologically equilibrated constrained mixture model for growth and remodeling of soft tissues
[EN] Growth and remodeling of soft tissues is a dynamic process and several theoretical frameworks have been developed to analyze the time-dependent, mechanobiological and/or biomechanical responses of these tissues to changes in external loads. Importantly, general processes can often be conveniently separated into truly non-steady contributions and steady-state ones. Depending on characteristic times over which the external loads are applied, time-dependent models can sometimes be specialized to respective time-independent formulations that simplify the mathematical treatment without compromising the goodness of the particularized solutions. Very few studies have analyzed the long-term, steady-state responses of soft tissue growth and remodeling following a direct approach. Here, we derive a mechanobiologically equilibrated formulation that arises from a general constrained mixture model. We see that integral-type evolution equations that characterize these general models can be written in terms of an equivalent set of time-independent, nonlinear algebraic equations that can be solved efficiently to yield long-term outcomes of growth and remodeling processes in response to sustained external stimuli. We discuss the mathematical conditions, in terms of orders of magnitude, that yield the particularized equations and illustrate results numerically for general arterial mechano-adaptations.Universidad Politecnica de Madrid; Ministerio de Educacion, Cultura y Deporte of Spain, Grant/Award Number: CAS17/00068; Ministerio de Economia y Competitividad of Spain, Grant/Award Number: DPI2015-69801-R; National Institutes of Health, Grant/Award Numbers: R01HL086418, R01HL105297, R01HL128602, U01HL116323Latorre, M.; Humphrey, JD. (2018). A mechanobiologically equilibrated constrained mixture model for growth and remodeling of soft tissues. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 98(12):2048-2071. https://doi.org/10.1002/zamm.20170030220482071981
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