Quasiperiodic Fibonacci Chain Research Articles

Diffusive transport in a quasiperiodic Fibonacci chain: Absence of many-body localization at weak interactions

We study high-temperature magnetization transport in a many-body spin-1/2 chain with on-site quasiperiodic potential governed by the Fibonacci rule. In the absence of interactions it is known that the system is critical with the transport described by a continuously varying dynamical exponent (from ballistic to localized) as a function of the on-site potential strength. Upon introducing weak interactions, we find that an anomalous noninteracting dynamical exponent becomes diffusive for any potential strength. This is borne out by a boundary-driven Lindblad dynamics as well as unitary dynamics, with agreeing diffusion constants. This must be contrasted to random potential where transport is subdiffusive at such small interactions. Mean-field treatment of the dynamics for small U always slows down the non-interacting dynamics to subdiffusion, and is therefore unable to describe diffusion in an interacting quasiperiodic system. Finally, briefly exploring larger interactions we find a regime of interaction-induced subdiffusive dynamics, despite the on-site potential itself having no "rare-regions".

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.

Engineering electronic states of periodic and quasiperiodic chains by buckling

The spectrum of spinless, non-interacting electrons on a linear chain that is buckled in a non-uniform, quasiperiodic manner is investigated within a tight binding formalism. We have addressed two specific cases, viz., a perfectly periodic chain wrinkled in a quasiperiodic Fibonacci pattern, and a quasiperiodic Fibonacci chain, where the buckling also takes place in a Fibonacci pattern. The buckling brings distant neighbors in the parent chain to close proximity, which is simulated by a tunnel hopping amplitude. It is seen that, in the perfectly ordered case, increasing the strength of the tunnel hopping (that is, bending the segments more) absolutely continuous density of states is retained towards the edges of the band, while the central portion becomes fragmented and host subbands of narrowing widths containing extended, current carrying states, and multiple isolated bound states formed as a result of the bending. A switching “on” and “off” of the electronic transmission can thus be engineered by buckling. On the other hand, in the second example of a quasiperiodic Fibonacci chain, imparting a quasiperiodic buckling is found to generate continuous subband(s) destroying the usual multifractality of the energy spectrum. We present exact results based on a real space renormalization group analysis, that is corroborated by explicit calculation of the two terminal electronic transport.

Quantum Fisher information for periodic and quasiperiodic anisotropic XY chains in a transverse field

In this work, the concept of quantum Fisher information (QFI) is used to characterize the quantum transitions and factorization transitions in one-dimensional anisotropic XY models with periodic coupling interaction and quasiperiodic one. For the periodic-two model, it is found that the Ising transition and anisotropic transition can be distinctively illustrated by the evolution of QFI and its first-order derivatives, confirmed additionally by the scaling behavior. For the quasiperiodic Fibonacci chain, the number of quantum phase transitions increases from one to the lth Fibonacci number $$F_{l}$$Fl when the anisotropic parameter $$\gamma $$? approaches zero. The phase diagram for the approximant $$F_{l}=8 $$Fl=8 is derived as an example. In addition, the factorization transition in the two models can be marked by the correlation quantity defined from the QFI. The present work demonstrates the implication of the QFI as a general fingerprint to characterize the quantum transitions and factorization transitions.

Electronic transmission in bent quantum wires

Electronic transmission in bent quantum wires modeled by the tight binding Hamiltonian, and clamped between ideal, semi-infinite leads is studied. The effect of ‘bending’ the chain is simulated by introducing a non-zero hopping between the extremities of the wire. It is seen that the proximity of the two ends gives rise to Fano line shapes in the transmission spectrum. Transmission properties for both an ordered lattice and a Fibonacci quantum wire are discussed. In the quasi-periodic Fibonacci chain, the proximity of the two ends of the chain closes all the gaps in the spectrum and the spectrum loses its Cantor set character.

Minimal multifractality in the spectrum of a quasiperiodic Hamiltonian

In many systems, the electronic energy spectrum is a continuous or singular continuous multifractal set with a distribution of scaling exponents. Here, we show that for a quasiperiodic potential, the multifractal energy spectrum can have a minimal dispersion of the scaling exponents. This is made by tuning the ratio between self-energies in a tigth-binding Hamiltonian defined in a quasiperiodic Fibonacci chain. The tuning is calculated numerically from a trace map, and coincides with the place where the scaling exponents of the map, obtained from cycles with period six and two, are equal. The diffusion of electronic wave packets also reflects the minimal multifractal fractal nature of the spectrum, by reducing intermittency. The present result can help to simplify the task of studying several problems in quasiperiodic systems, since the effects of multiscaling are better isolated.

Connection of one-dimensional aperiodic lattices to fibonacci-chains

One-dimensional aperiodic lattices of a row of materials are closely related to certain physical properties of the material. For characterizing the stacking of an aperiodic lattice built up of translationally equivalent layers it is required to find the relationship between characteristic data, derived directly from the intensity distribution on X-ray oscillation pattern of the disordered crystal region in question, and a corresponding quasiperiodic Fibonacci-chain, describing a longer part of the lattice.

Electronic properties of quasiperiodic Fibonacci chain including second-neighbor hopping in the tight-binding model

We present an exact real-space renormalization group (RSRG) scheme for the electronic Green’s functions of one-dimensional tight-binding systems having both nearest-neighbor and next-nearest-neighbor hopping integrals, and determine the electronic density of states for the quasiperiodic Fibonacci chain. This RSRG method also gives the Lyapunov exponents for the eigenstates. The Lyapunov exponents and the analysis of the flow pattern of hopping integrals under renormalization provide information about the nature of the eigenstates. Next we develop a 4 × 4 transfer matrix formalism for this generalized tight-binding system, which enables us to determine the wave function amplitudes. Interestingly, we observe that like the nearest-neighbor tight-binding Fibonacci chain, the present generalized tight-binding system also have critical eigenstates, Cantor-set energy spectrum and highly fragmented density of states. It indicates that these exotic physical properties are really the characteristics of the underlying quasiperiodic structure.

A natural class of generalized Fibonacci chains

In this paper we propose a class of substitution rules that generate quasiperiodic chains sharing their typical properties with the quasiperiodic Fibonacci chain. For a subclass we explicitly construct the atomic surface. Moreover, scaling properties of the energy spectrum are discussed in relation to the dynamics of trace maps.

Electronic stability of quasicrystals: application to flux phases

The energetic stability of disordered binary alloys in which electrons are interacting via a tight-binding Hamiltonian is considered. A phenomenological repulsive interatomic potential is also added to the Hamiltonian. For a weak potential, the gain in energy compared to the periodic linear chain is derived as a function of the electronic filling factor ν, and the disorder. For a given ν, the most stable structure is a quasiperiodic chain associated with ν and the atomic concentration. These results, which are exact for any concentration and filling factor, are illustrated on the quasiperiodic Fibonacci chain. As an application, we show that the preceding results favor the stability of uniform flux phases with a flux per plaquette Φ = ν.

Dynamic structure factor of a Fibonacci lattice: A renormalization-group approach.

We present a real-space renormalization-group method for evaluating the exact dynamic structure factor S(q,\ensuremath{\omega}) of a quasiperiodic Fibonacci chain. Contrary to earlier work that takes account only of the global aspects of the symmetry of the chain, our method additionally takes care of the local environmental aspects of the symmetry by separating the original lattice into a finite number of self-similar interpenetrating sublattices, followed by elimination of the coupling between them. Our method also yields correctly the positions of the Bragg peaks of the Fibonacci chain. Moreover, the present method allows the sites of the chain to be grouped into classes following a ``genealogical'' classification, the members of a given class being equivalent up to a certain length scale. Based on this classification, the proof of the existence of a key site, which has only been conjectured in our earlier work using numerical search, has been given.