In this work we investigate charge transport in one-dimensional (1D) insulators via semi-classical and perturbative renormalization group (RG) methods. We consider the problem of electron-electron, electron-phonon and electron-two-level system interactions. We show that non-linear collective modes such as polarons and solitons are reponsible for transport. We find a new excitation in the Mott insulator: the polaronic soliton. We discuss the differences between band and Mott insulators in terms of their spin spectrum and obtain the charge and spin gaps in each one of these systems. We show that electron-electron interactions provide strong renormalizations of the energy scales in the problem.
In this work we investigate charge transport in one-dimensional insulators via semiclassical and perturbative renormalization group methods. We consider the problem of electron-electron, electron-phonon and electron-two-level system interactions. We show that nonlinear collective modes such as polarons and solitons are responsible for transport. We find a new excitation in the Mott insulator: the polaronic soliton. We discuss fhe differences between band and Mott insulators in terms of their spin spectrum and obtain the charge and spin gaps in each one of these systems. We show that electron-electron interactions provide strong renormalizations of the energy scales in the problem.
We theoretically investigate the light absorption spectrum of two-dimensional (2D) Mott insulators. We employ the numerical diagonalization method to calculate the light absorption spectrum with using the effective Hamiltonian for the extended Hubbard model, which is valid when the on-site Coulomb interaction energy
U is much larger than the nearest-neighbor transfer integral
t and the nearest-neighbor Coulomb interaction energy
V. For
V=0, the absorption spectrum consists of a broad band with a width of about
16t and a sharp central peak, and the energy eigenstates contributing to the absorption spectrum do not have the antiferromagnetic (AF) spin order, when
U is sufficiently larger than
t. These features result from the spin-charge interplay inherent in the very strong correlation region where charge transfer term is dominant. With decreasing
U∕t, the peak structure in absorption spectrum becomes unclear and some low energy eigenstates have the AF spin order, as a result of the spin-spin interaction term. For large
V∕t, the dominant peak arises in the lower energy region of the spectrum. A large number of holon-doublon bound states, which have nearly the same charge but different spin structures, are responsible for this peak, in contrast to the conventional exciton state. This is also in contrast to the charge bound states in one-dimensional (1D) Mott insulators, where a single energy eigenstate dominates the optical transition moment as a result of the spin-charge separation. The essentially different absorption spectra between the 1D and 2D Mott insulators originate from the difference in the coupling between spin and charge degrees of freedom.
We applied a many-body Wannier functions method to theoretically calculate the excitonic optical conductivity spectrum and energy structure in a one-dimensional (1D) Mott insulator at absolute zero temperature with a large system size. Focusing on full charge fluctuations associated with holon and doublon pairs, we employ a charge model, which is interpreted as an effective model for investigating the photoexcitations of a 1D extended Hubbard model under a half-filling of the spin-charge separation. As a result, theoretical spectra with the appropriate broadenings qualitatively reproduce the recent experimental data of ET-
F2TCNQ at 294 K with and without a modulated electric field. Regarding the excitonic energy structure, we found that the excitons, particularly for even-parity, are weakly bound by many-body effects. This is also consistent with the fitting parameters reported in a recent experiment. Thus, the theoretical method presented in this paper is useful for understanding the physical roles of the charge fluctuations in many-body excited states of a 1D Mott insulator.
We employ dynamical density-matrix renormalization-group (DDMRG) and field-theory methods to determine the frequency-dependent optical conductivity in one-dimensional extended. half-filled Hubbard models. The field-theory approach is applicable to the regime of "small" Mott gaps which is the most difficult to access by DDMRG. For very large Mott gaps the DDMRG recovers analytical results obtained previously by means of strong-coupling techniques. We focus on exciton formation at energies below the onset of the absorption continuum. As a consequence of spin-charge separation, these Mott-Hubbard excitons are bound states of spinless, charged excitations ("holon-antiholon" pairs). We also determine exciton binding energies and sizes. In contrast to simple band insulators, we observe that excitons exist in the Mott-insulating phase only for a sufficiently strong intersite Coulomb repulsion. Furthermore, our results show that the exciton binding energy and size are not related in a simple way to the strength of the Coulomb interaction.