3,941 research outputs found
One-dimensional itinerant interacting non-Abelian anyons
We construct models of interacting itinerant non-Abelian anyons moving along
one-dimensional chains. We focus on itinerant Ising (Majorana) and Fibonacci
anyons, which are, respectively, related to SU(2)_2 and SU(2)_3 anyons and
also, respectively, describe quasiparticles of the Moore-Read and
Z_3-Read-Rezayi fractional quantum Hall states. Following the derivation of the
electronic large-U effective Hubbard model, we derive effective anyonic t-J
models for the low-energy sectors. Solving these models by exact
diagonalization, we find a fractionalization of the anyons into charge and
(neutral) anyonic degrees of freedom -- a generalization of spin-charge
separation of electrons which occurs in Luttinger liquids. A detailed
description of the excitation spectrum can be performed by combining spectra
for charge and anyonic sectors. The anyonic sector is the one of a squeezed
chain of localized interacting anyons, and hence is described by the same
conformal field theory (CFT), with central charge c=1/2 for Ising anyons and
c=7/10 or c=4/5 for Fibonacci anyons with antiferromagnetic or ferromagnetic
coupling, respectively. The charge sector is the spectrum of a chain of
hardcore bosons subject to phase shifts which coincide with the momenta of the
combined anyonic eigenstates, revealing a subtle coupling between charge and
anyonic excitations at the microscopic level (which we also find to be present
in Luttinger liquids), despite the macroscopic fractionalization. The combined
central charge extracted from the entanglement entropy between segments of the
chain is shown to be 1+c, where c is the central charge of the underlying CFT
of the localized anyon (squeezed) chain.Comment: 19 pages, 18 figure
Simulation of braiding anyons using Matrix Product States
Anyons exist as point like particles in two dimensions and carry braid
statistics which enable interactions that are independent of the distance
between the particles. Except for a relatively few number of models which are
analytically tractable, much of the physics of anyons remain still unexplored.
In this paper, we show how U(1)-symmetry can be combined with the previously
proposed anyonic Matrix Product States to simulate ground states and dynamics
of anyonic systems on a lattice at any rational particle number density. We
provide proof of principle by studying itinerant anyons on a one dimensional
chain where no natural notion of braiding arises and also on a two-leg ladder
where the anyons hop between sites and possibly braid. We compare the result of
the ground state energies of Fibonacci anyons against hardcore bosons and
spinless fermions. In addition, we report the entanglement entropies of the
ground states of interacting Fibonacci anyons on a fully filled two-leg ladder
at different interaction strength, identifying gapped or gapless points in the
parameter space. As an outlook, our approach can also prove useful in studying
the time dynamics of a finite number of nonabelian anyons on a finite
two-dimensional lattice.Comment: Revised version: 20 pages, 14 captioned figures, 2 new tables. We
have moved a significant amount of material concerning symmetric tensors for
anyons --- which can be found in prior works --- to Appendices in order to
streamline our exposition of the modified Anyonic-U(1) ansat
Superconvergence of Topological Entropy in the Symbolic Dynamics of Substitution Sequences
We consider infinite sequences of superstable orbits (cascades) generated by
systematic substitutions of letters in the symbolic dynamics of one-dimensional
nonlinear systems in the logistic map universality class. We identify the
conditions under which the topological entropy of successive words converges as
a double exponential onto the accumulation point, and find the convergence
rates analytically for selected cascades. Numerical tests of the convergence of
the control parameter reveal a tendency to quantitatively universal
double-exponential convergence. Taking a specific physical example, we consider
cascades of stable orbits described by symbolic sequences with the symmetries
of quasilattices. We show that all quasilattices can be realised as stable
trajectories in nonlinear dynamical systems, extending previous results in
which two were identified.Comment: This version: updated figures and added discussion of generalised
time quasilattices. 17 pages, 4 figure
User Story Software Estimation:a Simplification of Software Estimation Model with Distributed Extreme Programming Estimation Technique
Software estimation is an area of software engineering concerned with the identification, classification and measurement of features of software that affect the cost of developing and sustaining computer programs [19]. Measuring the software through software estimation has purpose to know the complexity of the software, estimate the human resources, and get better visibility of execution and process model. There is a lot of software estimation that work sufficiently in certain conditions or step in software engineering for example measuring line of codes, function point, COCOMO, or use case points.
This paper proposes another estimation technique called Distributed eXtreme Programming Estimation (DXP Estimation). DXP estimation provides a basic technique for the team that using eXtreme Programming method in onsite or distributed development. According to writer knowledge this is a first estimation technique that applied into agile method in eXtreme Programming
The quantum cat map on the modular discretization of extremal black hole horizons
Based on our recent work on the discretization of the radial AdS geometry
of extremal BH horizons,we present a toy model for the chaotic unitary
evolution of infalling single particle wave packets.
We construct explicitly the eigenstates and eigenvalues for the single
particle dynamics for an observer falling into the BH horizon, with time
evolution operator the quantum Arnol'd cat map (QACM).
Using these results we investigate the validity of the eigenstate
thermalization hypothesis (ETH), as well as that of the fast scrambling time
bound (STB).
We find that the QACM, while possessing a linear spectrum, has eigenstates,
which are random and satisfy the assumptions of the ETH.
We also find that the thermalization of infalling wave packets in this
particular model is exponentially fast, thereby saturating the STB, under the
constraint that the finite dimension of the single--particle Hilbert space
takes values in the set of Fibonacci integers.Comment: 28 pages LaTeX2e, 8 jpeg figures. Clarified certain issues pertaining
to the relation between mixing time and scrambling time; enhanced discussion
of the Eigenstate Thermalization Hypothesis; revised figures and updated
references. Typos correcte
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