Abstract:
Synchrotron X-ray diffraction experiment shows that the metal-insulator transition occurring in a ferromagnetic state of a hollandite K$_2$Cr$_8$O$_{16}$ is accompanied by a structural distortion from the tetragonal $I4/m$ to monoclinic $P112_{1}/a$ phase with a $\sqrt{2}\times\sqrt{2}\times 1$ supercell. Detailed electronic structure calculations demonstrate that the metal-insulator transition is caused by a Peierls instability in the quasi-one-dimensional column structure made of four coupled Cr-O chains running in the $c$-direction, leading to the formation of tetramers of Cr ions below the transition temperature. This furnishes a rare example of the Peierls transition of fully spin-polarized electron systems.

Abstract:
The one-dimensional extended Peierls-Hubbard model is studied at several band fillings using the density matrix renormalization group method. Results show that the ground state evolves from a Mott-Peierls insulator with a correlation gap at half-filling to a soliton lattice with a small band gap away from half-filling. It is also confirmed that the ground state of the Peierls-Hubbard model undergoes a transition to a metallic state at finite doping. These results show that electronic correlations effects should be taken into account in theoretical studies of doped polyacetylene. They also show that a Mott-Peierls theory could explain the insulator-metal transition observed in this material.

Abstract:
A quantum-mechanical stability analysis of metallic nanowires within the free-electron model is presented. The stability is determined by an interplay of electron-shell effects, the Rayleigh instability due to surface tension, and the Peierls instability. Although the latter effect limits the maximum length also for wires with "magic radii", it is found that nanowires in the micrometer range can be stable at room temperature.

Abstract:
Vanadium dioxide undergoes a first order metal-insulator transition at 340 K. In this work, we develop and carry out state of the art linear scaling DFT calculations refined with non-local dynamical mean-field theory. We identify a complex mechanism, a Peierls-assisted orbital selection Mott instability, which is responsible for the insulating M$_1$ phase, and furthermore survives a moderate degree of disorder.

Abstract:
In an attempt to clarify the nature of the crossover from a Peierls band insulator to a Mott Hubbard insulator, we analyze ground-state and spectral properties of the one-dimensional half-filled Holstein Hubbard model using exact diagonalization techniques.

Abstract:
On the basis of ab initio density functional theory (DFT) calculations, we derive the underlying microscopic model Hamiltonian for TiOCl, a unique system that shows two consecutive phase transitions from a Mott insulator to a spin-Peierls insulator through a structurally incommensurate phase. We show with our model that the presence of magnetic frustration in TiOCl leads to a competition with the spin-Peierls distortion, which results in the novel incommensurate phase. In addition, our calculations indicate that the spin-Peierls state is triggered by adiabatic phonons, which is essential for understanding the nature of the phase transition.

Abstract:
I construct the spectral function of the Luther-Emery model which describes one-dimensional fermions with one gapless and one gapped degree of freedom, i.e. superconductors and Peierls and Mott insulators, by using symmetries, relations to other models, and known limits. Depending on the relative magnitudes of the charge and spin velocities, and on whether a charge or a spin gap is present, I find spectral functions differing in the number of singularities and presence or absence of anomalous dimensions of fermion operators. I find, for a Peierls system, one singularity with anomalous dimension and one finite maximum; for a superconductor two singularities with anomalous dimensions; and for a Mott insulator one or two singularities without anomalous dimension. In addition, there are strong shadow bands. I generalize the construction to arbitrary dynamical multi-particle correlation functions. The main aspects of this work are in agreement with numerical and Bethe Ansatz calculations by others. I also discuss the application to photoemission experiments on 1D Mott insulators and on the normal state of 1D Peierls systems, and propose the Luther-Emery model as the generic description of 1D charge density wave systems with important electronic correlations.

Abstract:
In order to clarify the physics of the crossover from a Peierls band insulator to a correlated Mott-Hubbard insulator, we analyze ground-state and spectral properties of the one-dimensional half-filled Holstein-Hubbard model using quasi-exact numerical techniques. In the adiabatic limit the transition is connected to the band to Mott insulator transition of the ionic Hubbard model. Depending on the strengths of the electron-phonon coupling and the Hubbard interaction the transition is either first order or evolves continuously across an intermediate phase with finite spin, charge, and optical excitation gaps.

Abstract:
A local perturbation theory for the spectral analysis of the Schr\"odinger operator with two periodic potentials whose periods are commensurable has been constructed. It has been shown that the perturbation of the periodic 1D Hamiltonian by an additional small periodic potential leads to the following spectral deformation: all gaps in the spectrum of the unperturbed periodic Hamiltonian bear shifts while any band splits by arising additional gaps into a set of smaller spectral bands. The spectral shift, the position of additional gaps and their widths have been calculated explicitly. The applications to the operational regime of a nanoelectronic device based on Mott-Peierls stimulated transition have also been discussed.

Abstract:
Using a Fr?hlich Hamiltonian for the electron-lattice interaction, an expression for the Peierls phase transition temperature( TP)of metallic helical carbon nanotube (n1,n2)has been derived. As an illustration, the formula is used to estimate TP of metallic(n1,n2). The results indicate metallic(n1,n2)are stable against the Peierls distortion and preserve metallic property at and far bellow room temperature.