Symmetry crossover and excitation thresholds at the neutral-ionic transition of the modified Hubbard model

Exact ground states, charge densities and excitation energies are found using valence bond methods for N-site modified Hubbard models with uniform spacing. At the neutral-ionic transition (NIT), the ground state has a symmetry crossover in 4n, 4n+2 rings with periodic and antiperiodic boundary conditions, respectively. The modified Hubbard model has a continuous NIT between a diamagnetic band insulator on the paired side and a paramagnetic Mott insulator on the covalent side. The singlet-triplet (ST), singlet-singlet (SS) and charge gaps for finite N indicate that the ST and SS gaps close at the NIT with increasing U and that the charge gap vanishes only there. Finite-N excitations constrain all singularities to about 0.1t of the symmetry crossover. The NIT is interpreted as a localized ground state (gs) with finite gaps on the paired side and an extended gs with vanishing ST and SS gaps on the covalent side. The charge gap and charge stiffness indicate a metallic gs at the transition that, however, is unconditionally unstable to dimerization.Comment: 12 pages, including 8 figure

Density-matrix renormalization group studies of metal-halogen chains within a two-band extended Peierls-Hubbard model

The phase diagram of halogen-bridged mixed-valence metal complexes (MX) has been studied using a two-band extended Peierls-Hubbard model employing the recently developed density-matrix renormalization group method. We present the energies, charge- and spin-density distributions, bond orders, and charge-charge and spin-spin correlations, for the ground state, for different parameters of the model. The effects of bond alternation and site-diagonal distortion on the ground-state properties are considered in detail. We observe that the site-diagonal distortion plays a significant role in deciding the nature of the ground state of the system. We find that while the charge-density-wave (CDW) and bond-order-wave (BOW) phases can coexist, the CDW and SDW (spin-density-wave) phases are mutually exclusive in most cases. We have also studied the doped MX chains both with and without bond alternation and site-diagonal distortion in the CDW as well as SDW regimes. We find that the additional charges in the polarons and bipolarons for hole doping are confined to a few sites, in the presence of bond alternation and site-diagonal distortion. For electron doping, we find that the additional charge(s) is (are) smeared over the entire chain length, and although the energetics implies a disproportionation of the negatively charged bipolaron, the charge- and spin-density distributions do not reflect this. A positively charged bipolaron disproportionates into two polarons in the SDW region. There is also bond-order evidence for compression of the bond length for the positively charged polaronic and bipolaronic systems and an elongation of the bonds for systems with negatively charged polarons and bipolarons

Nonlinear optical properties of stilbene and azobenzene derivatives containing azaphosphane groups

We have studied the nonlinear optical (NLO) properties of some donor-acceptor molecules with stilbene and azobenzene molecules as backbone. We have used the nitro group as the acceptor and azaphosphane (R3P=N-) as the donor group. To study the effect of variation of NLO properties, we have replaced the substituents (Rs) connected to the phosphorus atom by methyl, amine and phenyl groups. We find that both first-order polarizability and hyperpolarizabilities are larger for stilbene derivatives and is maximum for the phenyl substitution. Second-order polarizability is higher for methyl substitution. We have also obtained the two-photon absorption cross-section for these molecules. We find that both one-photon and two-photon absorption cross-sections are maximum for the same excited state (first excited state in the case of stilbene and second excited state in the case of azobenzene derivatives)

A Density Matrix Renormalization Group Method Study of Optical Properties of Porphines and Metalloporphines

The symmetrized Density-Matrix-Renormalization-Group (DMRG) method is used to study linear and nonlinear optical properties of Free base porphine and metallo-porphine. Long-range interacting model, namely, Pariser-Parr-Pople (PPP) model is employed to capture the quantum many body effect in these systems. The non-linear optical coefficients are computed within correction vector method. The computed singlet and triplet low-lying excited state energies and their charge densities are in excellent agreement with experimental as well as many other theoretical results. The rearrangement of the charge density at carbon and nitrogen sites, on excitation, is discussed. From our bond order calculation, we conclude that porphine is well described by the 18-annulenic structure in the ground state and the molecule expands upon excitation. We have modelled the regular metalloporphine by taking an effective electric field due to the metal ion and computed the excitation spectrum. Metalloporphines have $D_{4h}$ symmetry and hence have more degenerate excited states. The ground state of Metalloporphines show 20-annulenic structure, as the charge on the metal ion increases. The linear polarizability seems to increase with the charge initially and then saturates. The same trend is observed in third order polarizability coefficients.Comment: 13 pages, 6 figure

Transition from band insulator to Mott insulator in one dimension: Critical behavior and phase diagram

We report a systematic study of the transition from a band insulator (BI) to a Mott insulator (MI) in a one-dimensional Hubbard model at half-filling with an on-site Coulomb interaction U and an alternating periodic site potential V. We employ both the zero-temperature density matrix renormalization group (DMRG) method to determine the gap and critical behavior of the system and the finite-temperature transfer matrix renormalization group method to evaluate the thermodynamic properties. We find two critical points at U = $U_c$ and U = $U_s$ that separate the BI and MI phases for a given V. A charge-neutral spin-singlet exciton band develops in the BI phase (U<$U_c$) and drops below the band gap when U exceeds a special point Ue. The exciton gap closes at the first critical point $U_c$ while the charge and spin gaps persist and coincide between $U_c$<U<$U_s$ where the system is dimerized. Both the charge and spin gaps collapse at U = $U_s$ when the transition to the MI phase occurs. In the MI phase (U>$U_s$) the charge gap increases almost linearly with U while the spin gap remains zero. These findings clarify earlier published results on the same model, and offer insights into several important issues regarding an appropriate scaling analysis of DMRG data and a full physical picture of the delicate nature of the phase transitions driven by electron correlation. The present work provides a comprehensive understanding for the critical behavior and phase diagram for the transition from BI to MI in one-dimensional correlated electron systems with a periodic alternating site potential.Comment: long version, 10 figure

Effects of Lattice and Molecular Phonons on Photoinduced Neutral-to-Ionic Transition Dynamics in Tetrathiafulvalene-pp-Chloranil

For electronic states and photoinduced charge dynamics near the neutral-ionic transition in the mixed-stack charge-transfer complex tetrathiafulvalene-$p$-chloranil (TTF-CA), we review the effects of Peierls coupling to lattice phonons modulating transfer integrals and Holstein couplings to molecular vibrations modulating site energies. The former stabilizes the ionic phase and reduces discontinuities in the phase transition, while the latter stabilizes the neutral phase and enhances the discontinuities. To reproduce the experimentally observed ionicity, optical conductivity and photoinduced charge dynamics, both couplings are quantitatively important. In particular, strong Holstein couplings to form the highly-stabilized neutral phase are necessary for the ionic phase to be a Mott insulator with large ionicity. A comparison with the observed photoinduced charge dynamics indicates the presence of strings of lattice dimerization in the neutral phase above the transition temperature.Comment: 9 pages, 7 figures, accepted for publication in J. Phys. Soc. Jp