Bond order wave (BOW) phase of the extended Hubbard model: Electronic solitons, paramagnetism, coupling to Peierls and Holstein phonons

The bond order wave (BOW) phase of the extended Hubbard model (EHM) in one dimension (1D) is characterized at intermediate correlation $U = 4t$ by exact treatment of $N$-site systems. Linear coupling to lattice (Peierls) phonons and molecular (Holstein) vibrations are treated in the adiabatic approximation. The molar magnetic susceptibility $\chi_M(T)$ is obtained directly up to $N = 10$. The goal is to find the consequences of a doubly degenerate ground state (gs) and finite magnetic gap $E_m$ in a regular array. Degenerate gs with broken inversion symmetry are constructed for finite $N$ for a range of $V$ near the charge density wave (CDW) boundary at $V \approx 2.18t$ where $E_m \approx 0.5t$ is large. The electronic amplitude $B(V)$ of the BOW in the regular array is shown to mimic a tight-binding band with small effective dimerization $\delta_{eff}$. Electronic spin and charge solitons are elementary excitations of the BOW phase and also resemble topological solitons with small $\delta_{eff}$. Strong infrared intensity of coupled molecular vibrations in dimerized 1D systems is shown to extend to the regular BOW phase, while its temperature dependence is related to spin solitons. The Peierls instability to dimerization has novel aspects for degenerate gs and substantial $E_m$ that suppresses thermal excitations. Finite $E_m$ implies exponentially small $\chi_M(T)$ at low temperature followed by an almost linear increase with $T$. The EHM with $U = 4t$ is representative of intermediate correlations in quasi-1D systems such as conjugated polymers or organic ion-radical and charge-transfer salts. The vibronic and thermal properties of correlated models with BOW phases are needed to identify possible physical realizations.Comment: 12 pages, 10 figure

Prediction of infrared light emission from pi-conjugated polymers: a diagrammatic exciton basis valence bond theory

There is currently a great need for solid state lasers that emit in the infrared, as this is the operating wavelength regime for applications in telecommunications. Existing $\pi$--conjugated polymers all emit in the visible or ultraviolet, and whether or not $\pi$--conjugated polymers that emit in the infrared can be designed is an interesting challenge. On the one hand, the excited state ordering in trans-polyacetylene, the $\pi$--conjugated polymer with relatively small optical gap, is not conducive to light emission because of electron-electron interaction effects. On the other hand, excited state ordering opposite to that in trans-polyacetylene is usually obtained by chemical modification that increases the effective bond-alternation, which in turn increases the optical gap. We develop a theory of electron correlation effects in a model $\pi$-conjugated polymer that is obtained by replacing the hydrogen atoms of trans-polyacetylene with transverse conjugated groups, and show that the effective on-site correlation in this system is smaller than the bare correlation in the unsubstituted system. An optical gap in the infrared as well as excited state ordering conducive to light emission is thereby predicted upon similar structural modifications.Comment: 15 pages, 15 figures, 1 tabl

Electron-electron interaction effects on the photophysics of metallic single-walled carbon nanotubes

Single-walled carbon nanotubes are strongly correlated systems with large Coulomb repulsion between two electrons occupying the same $p_z$ orbital. Within a molecular Hamiltonian appropriate for correlated $\pi$-electron systems, we show that optical excitations polarized parallel to the nanotube axes in the so-called metallic single-walled carbon nanotubes are to excitons. Our calculated absolute exciton energies in twelve different metallic single-walled carbon nanotubes, with diameters in the range 0.8 - 1.4 nm, are in nearly quantitative agreement with experimental results. We have also calculated the absorption spectrum for the (21,21) single-walled carbon nanotube in the E$_{22}$ region. Our calculated spectrum gives an excellent fit to the experimental absorption spectrum. In all cases our calculated exciton binding energies are only slightly smaller than those of semiconducting nanotubes with comparable diameters, in contradiction to results obtained within the {\it ab initio} approach, which predicts much smaller binding energies. We ascribe this difference to the difficulty of determining the behavior of systems with strong on-site Coulomb interactions within theories based on the density functional approach. As in the semiconducting nanotubes we predict in the metallic nanotubes a two-photon exciton above the lowest longitudinally polarized exciton that can be detected by ultrafast pump-probe spectroscopy. We also predict a subgap absorption polarized perpendicular to the nanotube axes below the lowest longitudinal exciton, blueshifted from the exact midgap by electron-electron interactions

Magnetic susceptibility of alkali-TCNQ salts and extended Hubbard models with bond order and charge density wave phases

The molar spin susceptibilities $\chi(T)$ of Na-TCNQ, K-TCNQ and Rb-TCNQ(II) are fit quantitatively to 450 K in terms of half-filled bands of three one-dimensional Hubbard models with extended interactions using exact results for finite systems. All three models have bond order wave (BOW) and charge density wave (CDW) phases with boundary $V = V_c(U)$ for nearest-neighbor interaction $V$ and on-site repulsion $U$. At high $T$, all three salts have regular stacks of $\rm TCNQ^-$ anion radicals. The $\chi(T)$ fits place Na and K in the CDW phase and Rb(II) in the BOW phase with $V \approx V_c$. The Na and K salts have dimerized stacks at $T < T_d$ while Rb(II) has regular stacks at 100K. The $\chi(T)$ analysis extends to dimerized stacks and to dimerization fluctuations in Rb(II). The three models yield consistent values of $U$, $V$ and transfer integrals $t$ for closely related $\rm TCNQ^-$ stacks. Model parameters based on $\chi(T)$ are smaller than those from optical data that in turn are considerably reduced by electronic polarization from quantum chemical calculation of $U$, $V$ and $t$ on adjacent $\rm TCNQ^-$ ions. The $\chi(T)$ analysis shows that fully relaxed states have reduced model parameters compared to optical or vibration spectra of dimerized or regular $\rm TCNQ^-$ stacks.Comment: 9 pages and 5 figure

Giant infrared intensity of the Peierls mode at the neutral-ionic phase transition

We present exact diagonalization results on a modified Peierls-Hubbard model for the neutral-ionic phase transition. The ground state potential energy surface and the infrared intensity of the Peierls mode point to a strong, non-linear electron-phonon coupling, with effects that are dominated by the proximity to the electronic instability rather than by electronic correlations. The huge infrared intensity of the Peierls mode at the ferroelectric transition is related to the temperature dependence of the dielectric constant of mixed-stack organic crystals.Comment: 4 pages, 4 figure

Dynamical Correlation Functions using the Density Matrix Renormalization Group

The density matrix renormalization group (DMRG) method allows for very precise calculations of ground state properties in low-dimensional strongly correlated systems. We investigate two methods to expand the DMRG to calculations of dynamical properties. In the Lanczos vector method the DMRG basis is optimized to represent Lanczos vectors, which are then used to calculate the spectra. This method is fast and relatively easy to implement, but the accuracy at higher frequencies is limited. Alternatively, one can optimize the basis to represent a correction vector for a particular frequency. The correction vectors can be used to calculate the dynamical correlation functions at these frequencies with high accuracy. By separately calculating correction vectors at different frequencies, the dynamical correlation functions can be interpolated and pieced together from these results. For systems with open boundaries we discuss how to construct operators for specific wavevectors using filter functions.Comment: minor revision, 10 pages, 15 figure

Spin-Peierls Dimerization of a s=1/2 Heisenberg Antiferromagnet on a Square Lattice

Dimerization of a spin-half Heisenberg antiferromagnet on a square lattice is investigated for several possible dimerized configurations, some of which are shown to have lower ground state energies than the others. In particular, the lattice deformations resulting in alternate stronger and weaker couplings along both the principal axes of a square lattice are shown to result in a larger gain in magnetic energy. In addition, a `columnar' configuration is shown to have a lower ground state energy and a faster increase in the energy gap parameter than a `staggered' configuration. The inclusion of unexpanded exchange coupling leads to a power law behaviour for the magnetic energy gain and energy gap, which is qualitatively different from that reported earlier. Instead of increasing as $\delta ^{x}$, the two quantities depend on $\delta$ as $\delta ^{\nu}/| \ln \delta | .$ This is true both in the near critical regime $(0\leq \delta \leq 0.1)$ as well as in the far regime $(0\leq \delta <1)$. It is suggested that the unexpanded exchange coupling is as much a source of the logarithmic dependence as a correction due to the contribution of umklapp processes. Staggered magnetization is shown to follow the same $\delta$-dependence in all the configurations in the small $\delta$-regime, while for $0\leq \delta <1$, it follows the power law $\delta ^{x}$.Comment: 12 pages, 7 Postscript figures, RevTex forma

Electronic polarization in pentacene crystals and thin films

Electronic polarization is evaluated in pentacene crystals and in thin films on a metallic substrate using a self-consistent method for computing charge redistribution in non-overlapping molecules. The optical dielectric constant and its principal axes are reported for a neutral crystal. The polarization energies P+ and P- of a cation and anion at infinite separation are found for both molecules in the crystal's unit cell in the bulk, at the surface, and at the organic-metal interface of a film of N molecular layers. We find that a single pentacene layer with herring-bone packing provides a screening environment approaching the bulk. The polarization contribution to the transport gap P=(P+)+(P-), which is 2.01 eV in the bulk, decreases and increases by only ~ 10% at surfaces and interfaces, respectively. We also compute the polarization energy of charge-transfer (CT) states with fixed separation between anion and cation, and compare to electroabsorption data and to submolecular calculations. Electronic polarization of ~ 1 eV per charge has a major role for transport in organic molecular systems with limited overlap.Comment: 10 revtex pages, 6 PS figures embedde