719 research outputs found
On the Entropy of a Two Step Random Fibonacci Substitution
Nilsson J. On the Entropy of a Two Step Random Fibonacci Substitution. Entropy. 2013;15(9):3312-3324.We consider a random generalization of the classical Fibonacci substitution. The substitution we consider is defined as the rule mapping, a → baa and b → ab, with probability , and → ba, with probability 1 – p for 0 < p < 1, and where the random rule is applied each time it acts on a . We show that the topological entropy of this object is given by the growth rate of the set of inflated random Fibonacci words, and we exactly calculate its value
On the Entropy of a Family of Random Substitutions
The generalised random Fibonacci chain is a stochastic extension of the
classical Fibonacci substitution and is defined as the rule mapping and with probability , where with
, and where the random rule is applied each time it acts on
a 1. We show that the topological entropy of this object is given by the growth
rate of the set of inflated generalised random Fibonacci words.Comment: A more appropriate tile and minor misprints corrected, compared to
the previous versio
Entanglement entropy in aperiodic singlet phases
We study the average entanglement entropy of blocks of contiguous spins in
aperiodic XXZ chains which possess an aperiodic singlet phase at least in a
certain limit of the coupling ratios. In this phase, where the ground state
constructed by a real space renormalization group method, consists
(asymptotically) of independent singlet pairs, the average entanglement entropy
is found to be a piecewise linear function of the block size. The enveloping
curve of this function is growing logarithmically with the block size, with an
effective central charge in front of the logarithm which is characteristic for
the underlying aperiodic sequence. The aperiodic sequence producing the largest
effective central charge is identified, and the latter is found to exceed the
central charge of the corresponding homogeneous model. For marginal aperiodic
modulations, numerical investigations performed for the XX model show a
logarithmic dependence, as well, with an effective central charge varying
continuously with the coupling ratio.Comment: 18 pages, 9 figure
Energy spectra of quasiperiodic systems via information entropy
We study the relationship between the electronic spectrum structure and the
configurational order of one-dimensional quasiperiodic systems. We take the
Fibonacci case as an specific example, but the ideas outlined here may be
useful to accurately describe the energy spectra of general quasiperiodic
systems of technological interest. Our main result concerns the {\em
minimization} of the information entropy as a characteristic feature associated
to quasiperiodic arrangements. This feature is shown to be related to the
ability of quasiperiodic systems to encode more information, in the Shannon
sense, than periodic ones. In the conclusion we comment on interesting
implications of these results on further developments on the issue of
quasiperiodic order.Comment: REVTeX 3.0, 8 pages, 3 figures available on request from FD-A
([email protected]), Phys Rev E submitted, MA/UC3M/02/9
Many-body localization in a quasiperiodic Fibonacci chain
We study the many-body localization (MBL) properties of a chain of
interacting fermions subject to a quasiperiodic potential such that the
non-interacting chain is always delocalized and displays multifractality.
Contrary to naive expectations, adding interactions in this systems does not
enhance delocalization, and a MBL transition is observed. Due to the local
properties of the quasiperiodic potential, the MBL phase presents specific
features, such as additional peaks in the density distribution. We furthermore
investigate the fate of multifractality in the ergodic phase for low potential
values. Our analysis is based on exact numerical studies of eigenstates and
dynamical properties after a quench
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