3,941 research outputs found

    One-dimensional itinerant interacting non-Abelian anyons

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    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

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    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

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    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

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    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

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    Based on our recent work on the discretization of the radial AdS2_2 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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