In this paper, we address the role of electron-electron interactions on the velocities of spin and charge transport in one-dimensional systems typified by conjugated polymers. We employ the Hubbard model to model electron-electron interactions. The recently developed technique of time dependent Density Matrix Renormalization Group (tdDMRG) is used to follow the spin and charge evolution in an initial wavepacket described by a hole doped in the ground state of the neutral system. We find that the charge and spin velocities are different in the presence of correlations and are in accordance with results from earlier studies; the charge and spin move together in the noninteracting picture while interaction slows down only the spin velocity. We also note that dimerization of the chain only weakly affects these velocities.
In this paper, we address the role of electron-electron interactions on the velocities of spin and charge transport in one-dimensional systems typified by conjugated polymers. We employ the Hubbard model to model electron-electron interactions. The recently developed technique of time dependent Density Matrix Renormalization Group (tdDMRG) is used to follow the spin and charge evolution in an initial wavepacket described by a hole doped in the ground state of the neutral system. We find that the charge and spin velocities are different in the presence of correlations and are in accordance with results from earlier studies; the charge and spin move together in the noninteracting picture while interaction slows down only the spin velocity. We also note that dimerization of the chain only weakly affects these velocities.
We investigate the effect of static electron-phonon coupling on real-time dynamics of spin and charge transport in $\ensuremath{\pi}$-conjugated polyene chains. The polyene chain is modeled by the Pariser-Parr-Pople Hamiltonian with dimerized nearest-neighbor parameter ${t}_{0}(1+\ensuremath{\delta})$ for short bonds and ${t}_{0}(1\ensuremath{-}\ensuremath{\delta})$ for long bonds, and long-range electron-electron interactions. We follow the time evolution of the spin and charge using time-dependent density matrix renormalization group technique when a hole is injected at one end of the chain in its ground state. We find that spin and charge dynamics followed through spin and charge velocities depend both on chain length and extent of dimerization $\ensuremath{\delta}$. Analysis of the results requires focusing on physical quantities such as average spin and charge polarizations, particularly in the large dimerization limit. In the dimerization range 0.0 $\ensuremath{\le}$ $\ensuremath{\delta}$ $\ensuremath{\le}$ 0.15, spin-charge dynamics is found to have a well-defined behavior, with spin-charge separation (measured as the ratio of charge velocity to spin velocity) as well as the total amount of charge and spin transported in a given time along the chain decreasing as dimerization increases. However, in the range 0.3 $\ensuremath{\le}$ $\ensuremath{\delta}$ $\ensuremath{\le}$ 0.5, it is observed that the dynamics of spin and charge transport becomes complicated. It is observed that, for large $\ensuremath{\delta}$ values, spin-charge separation is suppressed and the injected hole fails to travel the entire length of the chain.
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.
This thesis deals with out-of-equilibrium transport phenomena in strongly correlated low-dimensional fermionic systems, with special emphasis on π-conjugated molecular materials. The focus of this work is to study real-time dynamics of spin and charge transport in these systems in order to investigate non-equilibrium transport in single-molecule electronic and spintronic devices.
Chapter 1 describes the electronic structure and dynamics of strongly correlated fermionic systems in general, and in one-dimension, in particular. For this purpose, effective low-energy model Hamiltonians (used in this work) are discussed. Whenever applicable, approximate analytical and numerical methods commonly used in the literature to deal with these model Hamiltonians, are outlined. In the context of one-dimensional strongly correlated fermionic systems, analytical techniques like the Bethe ansatz and bosonization, and numerical procedures like exact diagonalization and DMRG, used for solving finite systems, are discussed in detail.
Chapter 2 provides an overview of the different zero-temperature (T = 0) time-dependent DMRG algorithms, which have been used to study out-of-equilibrium time-dependent phenomena in low-dimensional strongly correlated systems.
In Chapter 3 we employ the time-dependent DMRG algorithm proposed by Luo, Xiang and Wang [Phys. Rev. Lett. 91, 049701 (2003)], to study the role of dimerization and electronic correlations on the dynamics of spin-charge separation. We employ the H¨uckel and Hubbard models for our studies. We have modified the algorithm proposed by Luo et. al to overcome some of its limitations.
Chapter 4 presents a generalized adaptive time-dependent density matrix renormalization group (DMRG) scheme developed by us, called the Double Time Window Targeting (DTWT) technique, which is capable of giving accurate results with lesser computational resources than required by the existing methods. This procedure originates from the amalgamation of the features of pace keeping DMRG algorithm, first proposed by Luo et. al, [Phys.Rev. Lett. 91, 049701 (2003)], and the time-step targeting (TST) algorithm by Feiguin and White [Phys. Rev. B 72, 020404 (2005)].
In chapter 5 we apply the Double Time Window Targeting (DTWT) technique, which was discussed in the previous chapter, for studying real-time quantum dynamics of spin-charge separation in π-conjugated polymers. We employ the Pariser-Parr-Pople (PPP) model which has long-range electron-electron interactions. For investigating real-time dynamics of spin and charge transport, we inject a hole at one end of polyene chains of different lengths and study the temporal evolution of its spin and charge degrees of freedom, using the DTWT td-DMRG algorithm.
Chapter 6 we investigate the effect of terminal substituents on the dynamics of spin and charge transport in donor-acceptor substituted polyenes (D- (CH)x- A) chains, also known as push-pull polyenes. We employ long-range correlated model Hamiltonian for the D- (CH)x- A system and, real-time DMRG dynamics for…
In this paper we investigate the effect of terminal substituents on the dynamics of spin and charge transport in donor-acceptor substituted polyenes [D−−(CH)x−−A] chains, also known as push-pull polyenes. We employ a long-range correlated model Hamiltonian for the D−−(CH)x−−A system, and time-dependent density matrix renormalization group technique for time propagating the wave packet obtained by injecting a hole at a terminal site, in the ground state of the system. Our studies reveal that the end groups do not affect spin and charge velocities in any significant way, but change the amount of charge transported. We have compared these push-pull systems with donor-acceptor substituted polymethine imine (PMI), D−−(CHN)x−−A, systems in which besides electron affinities, the nature of pz orbitals in conjugation also alternate from site to site. We note that spin and charge dynamics in the PMIs are very different from that observed in the case of push-pull polyenes, and within the time scale of our studies, transport of spin and charge leads to the formation of a ``quasi-static'' state.
Discrepancies between the single-particle band structure and the exact many-particle behavior are particularly striking in one-dimensional systems. The one-dimensional alternating Hubbard model is especially interesting as a nontrivial model for conjugated polymer chains, such as polyacetelyne. We study this model for chains of 60 sites using the density-matrix renormalization-group method. We obtain the first electronic and magnetic excited-state energies at half filling as a function of an alternating hopping parameter and on-site electron-electron interaction. We also study the effect of the interaction on the dimerization and discuss its relation to the charge gap and spin triplet gap. In addition, we calculate the local spin and charge densities of some excited states, which manifest a clear crossover from bandlike to strongly correlated behavior.
Using the time-dependent density-matrix renormalization group, we study the time evolution of electronic wave packets in the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsion, U and V, respectively. As expected, the wave packets separate into spin-only and charge-only excitations (spin-charge separation). Charge and spin velocities exhibit nonmonotonic dependence on V. For small and intermediate values of V, both velocities increase with V. However, the charge velocity exhibits a stronger dependence than that of the spin, leading to a more pronounced spin-charge separation. Charge fractionalization, on the other hand, is weakly affected by V. The results are explained in terms of Luttinger liquid theory in the weak-coupling limit and an effective model in the strong-coupling regime.