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 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.
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 consider the quantum evolution and relaxation of an electron or hole which is coupled to a set of bath modes. In most applications the bath modes would be the vibronic coordinates but the model considered applies to any type of dynamic boson environment. The method is developed specifically for the problem of dynamic polaron formation in small nonperiodic systems. It can describe a broad group of experimental situations, including in particular electron localization in organics and polymeric materials and devices. The immediate bath is allowed to dissipate energy to a secondary bath. The bath obeys classical dynamics which puts some restriction on the range of validity of this approach. Using the density matrix formalism on a tight binding model consisting of a linear chain coupled to vibronic coordinates, we demonstrate in real time how the interaction with a dissipative bath makes the initial quantum distribution reach a steady-state population. This calculation is based on the Ehrenfest dynamics approximation. As an example we consider coupling at a single impurity site and find that for given parameters (bath coupling, site energy, and relaxation rate), the particle becomes dynamically localized in space on a particular time scale. This localized particle can be called a polaron. We define a population formation time in the same way as done in the experimental measurement. This formation time is studied as a function of the coupling strength, bandwidth, and energy dissipation rate. Energy dissipation plays a crucial role in the spatial localization process. The formation time shortens as the electron-vibration coupling increases, and as the intersite tunneling increases, but lengthens with impurity trap depth. Polaron formation is suppressed for sufficiently wide electronic bands.
We investigate the localization in a one-dimensional modified Peierls model with a non-adiabatic dynamic method. Different from the polaron scenario, here the localization stems from extensive conserved local quantities in the disorder-free lattice. Both the entanglement entropy and out-of-time-ordered correlator (OTOC) show the oscillating feature of dynamically generated localization. Although the strong interaction between electrons may suppress the dynamical features of the localization, but the effect of many-body localization is not observed. The role of disorder presented at finite temperature is discussed as well. The electrons diffuse in a classical manner. Benefitting from the indication of OTOC, it is found that the Anderson localization becomes dominant instead of dynamic localization as observed in disorder-free lattices.
We investigate the static and dynamical behavior of one-dimensional interacting fermions in disordered Hubbard chains contacted to semi-infinite leads. The chains are described via the repulsive Anderson-Hubbard Hamiltonian, using static and time-dependent lattice density-functional theory. The dynamical behavior of our quantum transport system is studied using an integration scheme available in the literature, which we modify via the recursive Lanczos method to increase its efficiency. To quantify the degree of localization due to disorder and interactions, we adapt the definition of the inverse participation ratio to obtain an indicator which is suitable for quantum transport geometries and can be obtained within density-functional theory. Lattice density-functional theories are reviewed and, for contacted chains, we analyze the merits and limits of the coherent-potential approximation in describing the spectral properties, with interactions included via lattice density-functional theory. Our approach appears to be able to capture complex features due to the competition between disorder and interactions. Specifically, we find a dynamical enhancement of delocalization in the presence of a finite bias and an increase of the steady-state current induced by interparticle interactions. This behavior is corroborated by results for the time-dependent densities and for the inverse participation ratio. Using short isolated chains with interaction and disorder, a brief comparative analysis between time-dependent density-functional theory and exact results is then given, followed by general concluding remarks.
The motion of polarons, which serve as charge carriers in conjugated polymers, is of fundamental importance for understanding transport properties of organic optoelectronic devices. We investigate the dynamics of a charged polaron in the presence of both electron-phonon and electron-electron interactions under the influence of an external electric field, which is modeled by the one-dimensional tight-binding Su-Schrieffer-Heeger (SSH) model supplemented with a Hubbard on-site repulsion term. For this many-body dynamical evolution problem, we develop an adaptive time-dependent density matrix renormalization group (t-DMRG) method in combination with a Newtonian equation of motion for atomic displacements. Our results show that the velocity of the polaron is suppressed by the on-site Coulomb interaction U. The polaron moves with a supersonic velocity, about four times the sound velocity at the small U limit, and approaches the sound velocity at the large U limit. Furthermore, the dependence of the polaron velocity and the polaron effective mass on the lattice structures are discussed.
The time evolution of two classes of systems is studied with real time molecular dynamics simulations. The first consists of a coupled electron-lattice system. For a periodic system, we present results for the time evolution of a one-dimensional system consisting of an electron, described by a tight-binding Hamiltonian, and a harmonic lattice, coupled by a deformation-type potential. We solve numerically the nonlinear system of equations of motion for this model in order to study the effects of varying the electronic effective mass for several initial conditions and coupling strengths. A large effective mass favors localized polaron formation for initially localized electrons. For initially extended electronic states, increasing the effective mass of an electron initially close to the bottom of the band makes localization more difficult, while for an initially highly excited electron, localized polaron formation is possible only when the electronic effective mass and the atomic masses of the lattice become of the same order. For a small parameter range, we find an impressive recurrence, a periodic and a complete exchange between the electronic and vibrational degrees of freedom of a small part of the initial electronic energy. The disordered case, described by a tight-binding model exhibiting metal-insulator transition (the diagonal matrix elements having a spatial variation incommensurate with the lattice), demonstrates the combined effects of disorder and electron-phonon interaction. The el-ph interaction has profound effects, especially on one-electron extended states just above the mobility edge, where the electronic states change from extended to localized. Polaron formation is facilitated close to the mobility edge and, in most cases, the localization length (lc) decreases upon increasing the disorder or el-ph coupling, as expected. However, for strongly localized states due to disorder or el-ph interaction, increase of el-ph coupling or disorder, respectively, results in an increase of lc. This increase is due to phonon assisted hopping. The second class of systems studied consists of carbon and hydrogen. We calculate phonon anharmonic effects in diamond and graphite using a tight-binding molecular dynamics scheme. Using one-phonon spectral intensities that have been calculated through the Fourier transform of the velocity-velocity correlation function, we study the temperature dependence of the phonon frequency shift and phonon linewidth. In the case of the zone-center optical mode of diamond where experimental data are available, our results are in good agreement with experiment. A tight-binding model for carbon-hydrogen interaction is developed and used in molecular dynamics simulations. The parameters are obtained by fitting to the electronic and vibrational properties of methane. The results obtained for hydrocarbon molecules are in good agreement with experimental data and first-principles results. Interstitial hydrogen in diamond is also studied with this model and the results are compared with available experimental and ab initio results. The case of hydrogenated amorphous carbon is considered as well.