arXiv subjects

M. Scheidler

Publications and source records attributed to M. Scheidler.

3 recordsLinked to original sources

arXiv1996

Optical absorption of non-interacting tight-binding electrons in a Peierls-distorted chain at half band-filling

In this first of three articles on the optical absorption of electrons in half-filled Peierls-distorted chains we present analytical results for non-interacting tight-binding electrons. We carefully derive explicit expressions for the current operator, the dipole transition matrix elements, and the optical absorption for electrons with a cosine dispersion relation of band width $W$ and dimerization parameter $δ$. New correction (``$η$''-)terms to the current operator are identified. A broad band-to-band transition is found in the frequency range $Wδ< ω< W$ whose shape is determined by the joint density of states for the upper and lower Peierls subbands and the strong momentum dependence of the transition matrix elements.

cond-mat↗

arXiv1996

Exact results for the optical absorption of strongly correlated electrons in a half-filled Peierls-distorted chain

In this second of three articles on the optical absorption of electrons in a half-filled Peierls-distorted chain we present exact results for strongly correlated tight-binding electrons. In the limit of a strong on-site interaction $U$ we map the Hubbard model onto the Harris-Lange model which can be solved exactly in one dimension in terms of spinless fermions for the charge excitations. The exact solution allows for an interpretation of the charge dynamics in terms of parallel Hubbard bands with a free-electron dispersion of band-width $W$, separated by the Hubbard interaction $U$. The spin degrees of freedom enter the expressions for the optical absorption only via a momentum dependent but static ground state expectation value. The remaining spin problem can be traced out exactly since the eigenstates of the Harris-Lange model are spin-degenerate. This corresponds to the Hubbard model at temperatures large compared to the spin exchange energy. Explicit results are given for the optical absorption in the presence of a lattice distortion $δ$ and a nearest-neighbor interaction $V$. We find that the optical absorption for $V=0$ is dominated by a peak at $ω=U$ and broad but weak absorption bands for $| ω-U | \leq W$. For an appreciable nearest-neighbor interaction, $V>W/2$, almost all spectral weight is transferred to Simpson's exciton band which is eventually Peierls-split.

cond-mat↗

arXiv1996

Optical absorption of strongly correlated half-filled Mott-Hubbard chains

In this last of three articles on the optical absorption of electrons in a half-filled Peierls-distorted chain we address the dimerized extended Hubbard model in the limit of a large on-site interaction $U$. When the Hubbard interaction is large both compared to the band width $W$ and the nearest neighbor interaction $V$ the charge dynamics is properly described by the Harris-Lange model. This model can be exactly mapped onto a model of free spinless Fermions in parallel (Hubbard-)bands of width $W$ which are eventually Peierls-split. To determine the coherent absorption features at low temperatures we design and employ the ``no-recoil approximation'' in which we assume that the momentum transfer to the spin degrees of freedom can only be $Δq_S=0$ or $Δq_S=π/a$ during an optical excitation. We present explicit analytical results for the optical absorption in the presence of a lattice dimerization $δ$ and a nearest-neighbor interaction $V$ for the Néel and dimer state. We find that the coherent part of the optical absorption for $V=0$ is given by a single peak at $ω=U$ and broad but weak absorption bands for $Wδ\leq |ω-U| \leq W$. The central peak at $ω=U$ only vanishes for $δ=0$ in the Néel state. For an appreciable nearest neighbor interaction $V>W/2$ almost all spectral weight is transferred to the $Δq_C=0$-exciton and the $Δq_C=π/a$-exciton whose relative spectral weights very sensitively depend on both the lattice and the spin dimerization of the ground state.

cond-mat↗