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arXiv:1103.1478 · Physical Review B

Effect of dimerization on dynamics of spin-charge separation in Pariser-Parr-Pople model: A time-dependent density matrix renormalization group study

Tirthankar Dutta, S. Ramasesha

Published Dec 27, 2011• 2 citations
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Abstract

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.

DOI
10.1103/physrevb.84.235147

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We investigate the effect of static electron-phonon coupling on real-time dynamics of spin and charge transport in \ensuremathπ\ensuremath{\pi}\ensuremathπ-conjugated polyene chains. The polyene chain is modeled by the Pariser-Parr-Pople Hamiltonian with dimerized nearest-neighbor parameter t0(1+\ensuremathδ){t}_{0}(1+\ensuremath{\delta})t0​(1+\ensuremathδ) for short bonds and t0(1\ensuremath−\ensuremathδ){t}_{0}(1\ensuremath{-}\ensuremath{\delta})t0​(1\ensuremath−\ensuremathδ) 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 \ensuremathδ\ensuremath{\delta}\ensuremathδ. 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≤\ensuremath{\le}\ensuremath≤ \ensuremathδ\ensuremath{\delta}\ensuremathδ \ensuremath≤\ensuremath{\le}\ensuremath≤ 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≤\ensuremath{\le}\ensuremath≤ \ensuremathδ\ensuremath{\delta}\ensuremathδ \ensuremath≤\ensuremath{\le}\ensuremath≤ 0.5, it is observed that the dynamics of spin and charge transport becomes complicated. It is observed that, for large \ensuremathδ\ensuremath{\delta}\ensuremathδ values, spin-charge separation is suppressed and the injected hole fails to travel the entire length of the chain.
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−−AD--{(\text{CH})}_{x}--AD−−(CH)x​−−A] chains, also known as push-pull polyenes. We employ a long-range correlated model Hamiltonian for the D−−(CH)x−−AD--{(\text{CH})}_{x}--AD−−(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−−AD--{(\text{CHN})}_{x}--AD−−(CHN)x​−−A, systems in which besides electron affinities, the nature of pz{p}_{z}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.
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 have carried out density-matrix renormalization group calculations on the ground state of long polyacene oligomers within a Pariser-Parr-Pople (PPP) Hamiltonian. The PPP model includes long-range electron correlations which are required for physically realistic modeling of conjugated polymers. We have obtained the ground-state energy as a function of the dimerization $\ensuremath{\delta}$ and various correlation functions and structure factors for $\ensuremath{\delta}=0$. From energetics, we find that the nature of the Peierls' instability in polyacene is conditional and strong electron correlations enhance the dimerization. The cis form of the distortion is favored over the trans form. However, from the analysis of correlation functions and associated structure factors, we find that polyacene is not susceptible to the formation of a bond order wave, spin-density wave, or a charge-density wave in the ground state.
The matrix product method (MPM) has been used in the past to generate variational Ans\"atze of the ground state (GS) of spin chains and ladders. In this paper we apply the MPM to study the GS of conjugated polymers in the valence bond basis, exploiting the charge and spin conservation as well as the electron-hole and spin-parity symmetries. We employ the U-VVV-$\ensuremath{\delta}$ Hamiltonian, which is a simplified version of the Pariser-Parr-Pople Hamiltonian. For several coupling constants U and V and dimerizations $\ensuremath{\delta},$ we compute the GS energy per monomer, which agrees within a 2--4 % accuracy with the density-matrix renormalization group results. We also show the evolution of the MP-variational parameters in the weak and strong dimerization regimes.
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…
We present a generalized adaptive time-dependent density matrix renormalization-group (DMRG) scheme, called the double time window targeting (DTWT) technique, which gives accurate results with nominal computational resources, within reasonable computational time. 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 algorithm by Feiguin and White [Phys. Rev. B 72, 020404 (2005)]. Using the DTWT technique, we study the phenomena of spin-charge separation in conjugated polymers (materials for molecular electronics and spintronics), which have long-range electron-electron interactions and belong to the class of strongly correlated low-dimensional many-body systems. The issue of real-time dynamics within the Pariser-Parr-Pople (PPP) model which includes long-range electron correlations has not been addressed in the literature so far. The present study on PPP chains has revealed that, (i) long-range electron correlations enable both the charge and spin degree of freedom of the electron, to propagate faster in the PPP model compared to Hubbard model, (ii) for standard parameters of the PPP model as applied to conjugated polymers, the charge velocity is almost twice that of the spin velocity, and (iii) the simplistic interpretation of long-range correlations by merely renormalizing the UUU value of the Hubbard model fails to explain the dynamics of doped holes/electrons in the PPP model.