Quantum dynamics on quasiperiodic geometries has recently gathered significant attention in ultracold atom experiments where nontrivial localized phases have been observed. One such quasiperiodic model is the so-called Fibonacci model. In this tight-binding model, noninteracting particles are subject to on-site energies generated by a Fibonacci sequence. This is known to induce critical states, with a continuously varying dynamical exponent, leading to anomalous transport. In this work, we investigate whether anomalous diffusion present in the noninteracting system survives in the presence of interactions and establish connections to a possible transition towards a localized phase. We investigate the dynamics of the interacting Fibonacci model by studying real-time spread of density-density correlations at infinite temperature using the dynamical typicality approach. We also corroborate our findings by calculating the participation entropy in configuration space and investigating the expectation value of local observables in the diagonal ensemble.
Quantum dynamics on quasiperiodic geometries has recently gathered significant attention in ultracold atom experiments where nontrivial localized phases have been observed. One such quasiperiodic model is the so-called Fibonacci model. In this tight-binding model, noninteracting particles are subject to on-site energies generated by a Fibonacci sequence. This is known to induce critical states, with a continuously varying dynamical exponent, leading to anomalous transport. In this work, we investigate whether anomalous diffusion present in the noninteracting system survives in the presence of interactions and establish connections to a possible transition towards a localized phase. We investigate the dynamics of the interacting Fibonacci model by studying real-time spread of density-density correlations at infinite temperature using the dynamical typicality approach. We also corroborate our findings by calculating the participation entropy in configuration space and investigating the expectation value of local observables in the diagonal ensemble.
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 a random potential where transport is subdiffusive at such small interactions. Mean-field treatment of the dynamics for small U always slows down the noninteracting 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.''
We investigate the quantum dynamics in a disordered electronic lattice by the time-dependent density matrix renormalization group algorithm. The on-site energy in the lattice follows the Fibonacci sequence and the electron off-diagonally couples to a sub-Ohmic phonon bath. It is found that the slope of the inverse participation ratio versus the coupling strength undergoes a sudden change that indicates a transition from static to dynamic localization, and that the generated polarons coherently diffuse via hopping-like processes, evidenced by the saturated entanglement entropy, providing a novel scenario for a transportation mechanism in strongly disordered systems. Moreover, the mean-square displacement is revealed to be insensitive to the coupling strength, implying the quantum diffusion behavior survives the energy disorder that prevails in real organic materials.
We study dephasing enhanced transport in boundary-driven quasiperiodic systems. Specifically, we consider dephasing modeled by current-preserving Lindblad dissipators acting on the noninteracting Aubry-Andr\'e-Harper and Fibonacci bulk systems. The former is known to undergo a critical localization transition with a suppression of ballistic transport above a critical value of the potential. At the critical point, the presence of nonergodic extended states yields anomalous subdiffusion. The Fibonacci model, on the other hand, yields anomalous transport with a continuously varying exponent depending on the potential strength. By computing the covariance matrix in the nonequilibrium steady state, we show that sufficiently strong dephasing always renders the transport diffusive. The interplay between dephasing and quasiperiodicity gives rise to a maximum of the diffusion coefficient for finite dephasing, which suggests that the combination of quasiperiodic geometries and dephasing can be used to control noise enhanced transport.
Quantum walk (QW), the quantum mechanical counterpart of classical random walk, has recently been studied in various fields. The evolution of the discrete time quantum walk can be described as follows: the walker changes its spin state by the coin operator C, then takes one step left or right according to its spin state. For homogeneous quantum walk, the coin operator is independent of time and the standard deviation of the position grows linearly in time. It is quadratically faster than that in the classical random walk. In this work, we numerically study the dynamical behaviors of spreading in a one-dimensional discrete time quasiperiodic quantum walk (DTQQW). The DTQQW is that the coin operator is dependent on time and takes two different coins C() and C() arranged in generalized Fibonacci (GF) sequences. The GF sequences are constructed from A by the recursion relation: AAmBn, BA, for m, n are positive integers. They can be classified into two classes according to the wandering exponent . For 0, they belong to the first class, and for 0, they belong to the second class. For one dimensional system, the behaviors of two classes of GF systems are different either for the electronic spectrum of an electron in quasiperiodic potentials or for the quantum phase transitions of the quasiperiodic spin chains. In this paper, we discuss the cases of two different C operators (C();C()) arranged in GF sequences and find that the spreading behaviors are superdiffusion (the standard deviation of the position ~t; 0:5 1) for the two classes of GF DTQQW. For the second class of GF DTQQW, the exponent values are larger than those of the first class of GF DTQQW in the case of two identical C operators. By exploring the probability distribution in the real space, we find that for the first class of GF DTQQW, the probability distributions are almost the same for different initial states and are similar to the classical Gaussian distribution. For the probability distributions of the second class of GF DTQQW, there are two peaks at the two edges and the height of the two peaks can be different for different initial states. They are similar to the ballistic distribution of the homogeneous quantum walk. Therefore, we conclude that for the first class of GF DTQQW, the spreading behaviors are close to those of the classical random walk ( = 0:5) while for the second class of GF DTQQW, they are close to those of the homogeneous quantum walk ( = 1). This result is quite different from the characteristics of the quantum phase transitions in two classes of GF quasiperiodic quantum spin chains.
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.
One dimensional quasiperiodic systems have been a vibrant topic of theorical research for physicists and mathematicians alike, owing to their highly non-trivial localization properties and the fractal nature of their energy spectrum.The most paradigmatic of such systems, the Aubry-André-Harper (AAH) model, is well known for suffering a localization transition when the potential strength is increased, in which its eigenstates go from extended to localized, similarly to Anderson phase transition which occurs in disordered three-dimensional systems.The localization of the eigenstates has dramatic effects in the transport regime of the system.In this dissertation, we used numerical simulations to study the transport properties of boundary-driven fermionic quantum chains subject to two choices for the on-site potential: the aforementioned AAH model and the Fibonacci model.The transport regime is classified via the scaling of the particle current with the system size in the non-equilibrium steady state (NESS), which we calculate numerically.Our main focus was the interplay between the quasiperiodic potential and dephasing noise.We showed that even though dephasing always leads to diffusive behaviour, the transport properties of the system are still visibly affected by localization properties of the eigenstates when the coupling to dephasing is small.This influence is reflected in the scaling of the diffusion constant with the coupling.In particular, we showed that, in the localized phase of the AAH model and in the subdifusive phase of the Fibonacci model, dephasing noise may actually lead to an enhanced transport, that is, a larger value of the current compared to the zero dephasing case.