In this paper,we use the extended SSH Hamilton model plus Long-range electron correlation Hamiltonian to study change of long-range correlation energy with time in a finite length trans-polyacetylene chain with free boundaries under adiabatic condition in terms of dynamic method.We calculated the effect of the long-rang electron correlation on the polaron dynamics.It is found that the long-rang correlation shows a non-periodic damped oscillation with time when we add an electron or a hole in the trans-polyacetylene chain.After some time,the long-rang correlation energy approaches a constant and at the same time the stable configuration of the lattice is reached.The time that the long-rang correlation energy tends to a constant will decrease with increasing the lattice numbers.
In this paper,we use the extended SSH Hamilton model plus Long-range electron correlation Hamiltonian to study change of long-range correlation energy with time in a finite length trans-polyacetylene chain with free boundaries under adiabatic condition in terms of dynamic method.We calculated the effect of the long-rang electron correlation on the polaron dynamics.It is found that the long-rang correlation shows a non-periodic damped oscillation with time when we add an electron or a hole in the trans-polyacetylene chain.After some time,the long-rang correlation energy approaches a constant and at the same time the stable configuration of the lattice is reached.The time that the long-rang correlation energy tends to a constant will decrease with increasing the lattice numbers.
Abstract We study the role of dynamic correlation and polaronic effects on the correlational properties of a GaAs-based electron quantum wire at finite-temperature T. The dynamics of electron correlations is incorporated through the self-consistent mean-field approximation of Hasegawa and Shimizu (the qSTLS theory) and the polaronic effects via the Fröhlich interactions. Results are presented for the static correlation functions, dynamic structure factor and electron’s contact probability over a wide range of T and electron number density r s . We find that for a fixed wire width b and T, electrons undergo a transition from the quantum liquid to Wigner crystal state due to the dynamics of severely correlated electrons at a critical r s = r s c . The inclusion of polaronic effects along with the conventional electron-electron interactions tends to increase r s c significantly at each T ultimately improving the quantum phase diagram. The electron’s contact probability exhibits a non-monotonic T-dependence which remains positive over a broader range of r s owing to the inclusion of polaronic effects. Besides, we explore the effect of phonon contribution on the plasmon energy of the quantum wire at non-zero T and find that there is splitting in the energy into two branches namely, plasmonlike and phononlike with former having energy lower than the latter. Both of the energy modes show consistent blue shift with rise in T, get damp at a critical wave vector q c , and q c decreases with T. Finally, we calculate the finite-T polaronic contribution to the free energy whose magnitude increases with T as r s → 0 and it becomes almost constant at sufficiently high r s .
The polaron features for long-range electron–phonon interaction are investigated by extending a variational approach previously proposed for the study of systems with local coupling. The ground state spectral weight, the average kinetic energy, the mean number of phonons, and the electron–lattice correlation function are discussed for a wide range of model parameters focusing on the adiabatic regime and comparing the results with the short-range case (Holstein model). A strong mixing of electronic and phononic degrees of freedom for small values of the electron–phonon coupling constant is found in the adiabatic case due to the long-range interaction. Finally a polaron ‘phase diagram’ is proposed.
We explore the quasiparticle properties of lattice polarons on the basis of a quite general electron-phonon Hamiltonian with a long-range displacement-type interaction. To treat the dynamical quantum phonons without significant loss of accuracy we adapt an exact Lanczos diagonalization method and compute various static and dynamical quantities, such as the electron-lattice correlation function, the polaron band dispersion, the effective polaron mass, the kinetic energy, the single-particle spectral function, and the optical conductivity, on finite one-dimensional lattices for a wide range of model parameters. We compare the results with those obtained for the standard Holstein model with short-range electron-phonon interaction only.
We study theoretically polydiacetylene chains diluted in their monomer matrix. We employ the density-matrix renormalisation group method (DMRG) on finite chains to calculate the ground state and low-lying excitations of the corresponding Peierls–Hubbard-Ohno Hamiltonian that is characterised by the electron transfer amplitude t 0 between nearest-neighbours, by electron–phonon coupling constant α, by Hubbard interaction U, and by long-range interaction V. We treat lattice relaxation in the adiabatic limit, i.e., we calculate the polaronic lattice distortions for each excited state. We present accurate DMRG results for the single-particle gap, the singlet exciton, the triplet ground state and its optical excitation, and find a good agreement with experimental data for PDA–3BCMU chains. Using a fairly stiff spring constant, the length of our unit cell is about 1% larger than observed in experiment.
We present the numerically exact ground-state energy, effective mass, and isotope exponents of a one-dimensional lattice polaron, valid for any range of electron-phonon interaction, applying a continuous-time quantum Monte Carlo (QMC) technique in a wide range of coupling strength and adiabatic ratio. The QMC method is free from any systematic finite-size and finite-time-step errors. We compare our numerically exact results with analytical weak-coupling theory and with the strong-coupling $1∕\ensuremath{\lambda}$ expansion. We show that the exact results agree well with the canonical Fr\"ohlich and Holstein-Lang-Firsov theories in the weak and strong coupling limits, respectively, for any range of interaction. We find a strong dependence of the polaron dynamics on the range of interaction. An increased range of interaction has a similar effect to an increased (less adiabatic) phonon frequency: specifically, a reduction in the effective mass.
Coupled-cluster theory with connected single and double excitation operators (CCSD) and related approximations, such as linearized CCSD, quadratic configuration interaction with single and double excitation operators, coupled-cluster with connected double excitation operator (CCD), linearized CCD, approximate CCD, and second- and third-order many-body perturbation theories, are formulated and implemented for infinitely extended one-dimensional systems (polymers), on the basis of the periodic boundary conditions and distance-based screening of integrals, density matrix elements, and excitation amplitudes. The variation of correlation energies with the truncation radii of short- and long-range lattice sums and with the number of wave vector sampling points in the first Brillouin zone is examined for polyethylene, polyacetylene, and polyyne, and is shown to be a function of the degree of pi-electron conjugation or the fundamental band gaps. The t2 and t1 amplitudes in the atomic orbital (AO) basis are obtained by first computing the t amplitudes in the Bloch-orbital basis and subsequently back-transforming them into the AO basis. The plot of these AO-based t amplitudes as a function of unit cells also indicates that the t2 amplitudes of polyacetylene and polyyne exhibit appreciably slower decay than those of polyethylene, although the asymptotic decay behavior is invariably 1/r3. The AO-based t1 amplitudes appear to correlate strongly with the electronic structure, and they decay seemingly exponentially for polyethylene whereas they stay at a constant magnitude across the seventh nearest neighbors of polyacetylene and polyyne, which attests to far reaching effects of nondynamical electron correlation mediated by orbital rotation. Nonetheless, the unit cell contributions to the correlation energies taper below 10(-6) hartree after 15 A for all three polymers. The basis set dependence of the decay behavior of t2 amplitudes is also examined for linear hydrogen fluoride polymer (HF)infinity and linear beryllium polymer (Be)infinity employing the STO-3G, 6-31G, and 6-31G* basis sets, and proves to be rather small.