Unfolding spinor wavefunctions and expectation values of general operators: Introducing the unfolding-density operator

We show that the spectral weights $W_{m\vec K}(\vec k)$ used for the unfolding of two-component spinor eigenstates $| {\psi_{m\vec K}^\mathrm{SC}} > = | \alpha > | {\psi_{m\vec{K}}^\mathrm{SC, \alpha}} > + | \beta > | {\psi_{m\vec{K}}^\mathrm{SC, \beta}} >$ can be decomposed as the sum of the partial spectral weights $W_{m\vec{K}}^{\mu}(\vec k)$ calculated for each component $\mu = \alpha, \beta$ independently, effortlessly turning a possibly complicated problem involving two coupled quantities into two independent problems of easy solution. Furthermore, we define the unfolding-density operator $\hat{\rho}_{\vec{K}}(\vec{k}_{i}; \, \varepsilon)$, which unfolds the primitive cell expectation values $\varphi^{pc}(\vec{k}; \varepsilon)$ of any arbitrary operator $\mathbf{\hat\varphi}$ according to $\varphi^{pc}(\vec{k}_{i}; \varepsilon) = \mathit{Tr}(\hat{\rho}_{\vec{K}}(\vec{k}_{i}; \, \varepsilon)\,\,\hat{\varphi})$. As a proof of concept, we apply the method to obtain the unfolded band structures, as well as the expectation values of the Pauli spin matrices, for prototypical physical systems described by two-component spinor eigenfunctions

Mott-Peierls Transition in the extended Peierls-Hubbard model

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.Comment: 4 pages with 3 embedded eps figure

Path Integral Description of a Semiclassical Su-Schrieffer-Heeger Model

The electron motion along a chain is described by a continuum version of the Su-Schrieffer-Heeger Hamiltonian in which phonon fields and electronic coordinates are mapped onto the time scale. The path integral formalism allows us to derive the non local source action for the particle interacting with the oscillators bath. The method can be applied for any value of the {\it e-ph} coupling. The path integral dependence on the model parameters has been analysed by computing the partition function and some thermodynamical properties from $T= 1K$ up to room temperature. A peculiar upturn in the low temperature {\it heat capacity over temperature} ratio (pointing to a glassy like behavior) has been ascribed to the time dependent electronic hopping along the chain