One-dimensional Peierls-Hubbard Model Research Articles

Optical Response of Polarons and Solitons in One-Dimensional Peierls–Hubbard Model

We investigate optical properties of polarons and solitons in one-dimensional (1D) Peierls–Hubbard model by using the density matrix renormalization group method combined with the adiabatic approxi...

Cellular dynamical mean-field study of the one-dimensional Peierls Hubbardmodel

Cellular dynamical mean-field study of the one-dimensional Peierls Hubbardmodel

Direct evidence of overdamped Peierls-coupled modes in the temperature-induced phase transition in tetrathiafulvalene-chloranil

In this paper, we elucidate the optical response resulting from the interplay of charge distribution (ionicity) and Peierls instability (dimerization) in the neutral-ionic ferroelectric phase transition of tetrathiafulvalene-chloranil, a mixed-stack quasi-one-dimensional charge-transfer crystal. We present far-infrared reflectivity measurements down to $5\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{\ensuremath{-}1}$ as a function of temperature above the phase transition (300--82 K). The coupling between electrons and lattice phonons in the pretransitional regime is analyzed on the basis of phonon eigenvectors obtained through quasiharmonic lattice dynamics, combined with the results of exact numerical diagonalization of the one-dimensional Peierls-Hubbard model. The resulting multiphonon Peierls coupling leads upon approaching the phase transition to a progressive shift of spectral weight and of the coupling strength toward the phonons at lower frequencies, ending in a soft-mode behavior only for the lowest-frequency phonon near the transition temperature. Moreover, in the proximity of the phase transition, the lowest-frequency phonon becomes overdamped due to anharmonicity induced by its coupling to electrons. The implications of these findings for the neutral-ionic transition mechanism are discussed.

The Peierls–Hubbard model at weak coupling

We investigate the Peierls transition in the one-dimensional Peierls–Hubbardmodel at half-filling in the adiabatic approximation for the lattice.Depending on the value of the electron–lattice coupling constantg the equilibrium dimerization can be either enhanced or suppressed by the Hubbard interactionU. Applying second-order perturbation theory we determine the critical valuegc = 0.689 348 below which the Hubbard interaction enhances the dimerization.

Dynamical density-matrix renormalization-group method

A density-matrix renormalization-group (DMRG) method for calculating dynamical properties and excited states in low-dimensional lattice quantum many-body systems is presented. The method is based on an exact variational principle for dynamical correlation functions and the excited states contributing to them. This dynamical DMRG is an alternate formulation of the correction vector DMRG but is both simpler and more accurate. The finite-size scaling of spectral functions is discussed and a method for analyzing the scaling of dense spectra is described. The key idea of the method is a size-dependent broadening of the spectrum. The dynamical DMRG and the finite-size scaling analysis are demonstrated on the optical conductivity of the one-dimensional Peierls-Hubbard model. Comparisons with analytical results show that the spectral functions of infinite systems can be reproduced almost exactly with these techniques. The optical conductivity of the Mott-Peierls insulator is investigated and it is shown that its spectrum is qualitatively different from the simple spectra observed in Peierls (band) insulators and one-dimensional Mott-Hubbard insulators.

Quantum Phase Transitions in One-Dimensional Peierls-Hubbard Model with Next-Nearest-Neighbor Hopping Integrals

Two kinds of phase transitions observed in the half-filled Peierls-Hubbard chain with the next-nearest-neighbor hopping integral are investigated. In the uniform case, according to the conformal field theory prediction, we numerically determine a phase boundary between the spin-fluid and dimer states. Then, the criticality of the spin-Peierls transition (i.e., powerlaw dependences of the energy gain and spin gap on the lattice dimerization parameter) is argued on the phase boundary.

Quantum phase transitions of the one-dimensional Peierls-Hubbard model with next-nearest-neighbor hopping integrals

We investigate two kinds of quantum phase transitions observed in the one-dimensional half-filled Peierls-Hubbard model with the next-nearest-neighbor hopping integral in the strong-coupling region $U\ensuremath{\gg}t$, ${t}^{\ensuremath{'}}$ [$t$ ${(t}^{\ensuremath{'}})$, nearest- (next-nearest-) neighbor hopping; $U$, on-site Coulomb repulsion]. In the uniform case, with the help of the conformal field theory prediction, we numerically determine a phase boundary ${t}_{\mathrm{c}}^{\ensuremath{'}}(U/t)$ between the spin-fluid and the dimer states, where a bare coupling of the marginal operator vanishes and the low-energy and long-distance behaviors of the spin part are described by a free-boson model. To exhibit the conformal invariance of the systems on the phase boundary, a multiplet structure of the excitation spectrum of finite-size systems and a value of the central charge are also examined. The critical phenomenological aspect of the spin-Peierls transitions accompanied by the lattice dimerization is then argued for the systems on the phase boundary; the existence of logarithmic corrections to the power-law behaviors of the energy gain and the spin gap (i.e., the Cross-Fisher scaling law) are discussed.

Solitons in the one-dimensional Peierls-Hubbard model

A variational method is used to study solitons in the framework of the one-dimensional Peierls-Hubbard model. Both the structure of a neutral soliton and the soliton-induced optical transitions are calculated. The comparison of the results with exact numerical calculations and experimentals data on trans-polyacetylene confirm not only the validity of the variational approach, but also the necessity of including correlation effects explicity.

The metal-insulator transition in polyacetylene: variational study of the Peierls-Hubbard model

The one-dimensional Peierls-Hubbard model is shown to describe in a natural way the metal-insulator transition observed in polyacetylene as a function of doping. A single set of parameters is able account for the insulating state at half filling (dimerization, optical gap), charged solitons close to half filling and a transition to a state with vanishing gap at a doping concentration of about 8%. A brief summary of other scenarios relying on disorder and interchain coupling is also presented.

Excitations of the one-dimensional, two-band Peierls-Hubbard model at three-quarters filling in the large-U limit.

We investigate the ground state and the excitation spectrum associated with the localized defect states of the three-quarter-filled, one-dimensional Peierls-Hubbard model. In the continuum limit with an infinite, on-site electron-electron repulsion energy U, the Hamiltonian is mapped onto the N=1 Gross-Neveu model, in which irrationally charged soliton-antisoliton pairs are formed upon doping, while polarons are unstable. Corrections due to finite-U effects are discussed. However, discreteness effects are found to support excitations absent from the continuum field theory. In particular, for large band separation a novel type of polaron can be formed with a highly localized electronic wave function surrounded by an extended pattern of local lattice distortion.

Variational treatment of the one-dimensional Peierls-Hubbard model: Lattice dimerization and solitons

The one-dimensional SSH Hamiltonian supplemented by an on-site Coulomb interaction is investigated using the Gutzwiller Ansatz. The various expectation values for the correlated ground state are evaluated numerically (Hubbard-Stratonovich transformation and Monte Carlo simulation). Within the parameter region studied, the lattice dimerization (for the half-filled band) has lower energy than the spin-density wave ground state. Preliminary results for charged and neutral solitons show that these two inhomogeneous configurations are more and more distinct, both in size and energy, as the Hubbard parameter U increases.

Quantum lattice fluctuations in the one-dimensional Peierls-Hubbard model.

The effect of quantum lattice fluctuations is investigated in a half-filled one-dimensional Peierls-Hubbard model. The nonadiabatic effects due to finite phonon frequency \ensuremath{\omega} are treated by introducing the polaronic transformation and the squeezed-phonon state. The electronic correlations are treated by means of a modified Gutzwiller approach and a unified description for the long-range charge-density-wave (CDW) ordering state and the short-range antiferromagnetic correlated state has been developed. The main result is a rather good description of the continuous variation of the dimerization as functions of the Hubbard U and \ensuremath{\omega} is given, which is in good agreement with that of the numerical simulations. The results of the squeezed-polaron theory are shown to be better than those of the ordinary polaron theory. A continuous phase transition is found between the long-range CDW ordering state and the short-range antiferromagnetic correlated state with a transition point different from the prediction of the Hartree-Fock decoupling. The effect of quantum lattice fluctuations on the transition point is also discussed.

Pair-creation path of doubly charged spinless soliton through photoexcitation in halogen-bridged metal complexes

To clarify the lattice relaxation paths of the photo-generated charge transfer excitation in halogen-bridged mixed-valence metal complexes, we study the ground and excited states of a one-dimensional Peierls-Hubbard model with half-filled electrons. A pair of doubly charged solitons is shown to be the lowest excited state and causes a photo-induced absorption (PIA) with an energy of about half of the gap, while a distant pair of polarons is shown to give the PIA observed by Kurita et al. The self-trapped exciton is shown to be next lowest excited state separated from this soliton pair only by a small barrier in agreement with the recent experiments.