We derive an exact solution for the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ of one hole in the Holstein $t\text{\ensuremath{-}}J$ model in the framework of dynamical mean-field theory. We investigate the magnetic and phonon features associated with polaron formation as a function of the exchange coupling
J, electron-phonon interaction $\ensuremath{\lambda}$, and temperature. Our solution directly relates the features of the optical conductivity to excitations in the single-particle spectral function, revealing two distinct mechanisms of closing and filling of the optical pseudogap that take place upon varying the microscopic parameters. We show that the optical absorption at the polaron crossover is characterized by a coexistence of a magnon peak at low frequency and a broad polaronic band at higher frequency. An analytical expression for $\ensuremath{\sigma}(\ensuremath{\omega})$ valid in the polaronic regime is presented.
Applying newly developed dynamical density matrix renormalization group techniques at zero and finite temperatures to a Hubbard-Holstein model at half filling, we examine the optical conductivity of a typical one-dimensional Mott insulator
Sr2CuO3. We find a set of parameters in the Hubbard-Holstein model, which can describe optical conductivity for both Mott-gap excitation in the high-energy region and phonon-assisted spin excitation in the low-energy region. We also find that electron-phonon interaction gives additional broadening in the temperature dependence of the Mott-gap excitation.
The real part of optical conductivity,
Reσ(ω), of the Mott insulators has a large amount of information on how spin and charge degrees of freedom interact with each other. By using the time-dependent density-matrix renormalization group, we study
Reσ(ω) of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of
Reσ(ω) not only for the two-dimensional square lattice but also for two- and four-leg ladders. For the square lattice, however, we do not clearly find a gap between an excitonic peak and continuum band, which indicates that a bound state is not well-defined. The emergence of an excitonic peak in
Reσ(ω) implies the formation of a spin polaron. Examining the dependence of
Reσ(ω) on the on-site Coulomb interaction and next-nearest neighbor hoppings, we confirm that an excitonic peak is generated from a magnetic effect. Electron scattering due to an electron-phonon interaction is expected to easily suppress an excitonic peak since spectral width of an excitonic peak is very narrow. Introducing a large broadening in
Reσ(ω) by modeling the electron-phonon coupling present in La
2CuO
4 and Nd
2CuO
4, we obtain
Reσ(ω) comparable with experiments.
The optical conductivity of the weakly doped two-dimensional repulsive Hubbard model on the square lattice with the nearest and next-nearest hoppings is calculated within the generalized dynamical mean-field $(\mathrm{DMFT}+{\ensuremath{\sum}}_{\mathbf{p}})$ approach, which includes correlation length scale $\ensuremath{\xi}$ into the standard DMFT equations via the momentum dependent self-energy ${\ensuremath{\sum}}_{\mathbf{p}}$, with a full account of appropriate vertex corrections. This approach takes into consideration the nonlocal dynamical correlations induced, e.g., by short-ranged collective spin-density-wavelike antiferromagnetic spin fluctuations, which (at high enough temperatures) can be viewed as a quenched Gaussian random field with finite correlation length $\ensuremath{\xi}$. The DMFT effective single-impurity problem is solved by numerical renormalization group. We consider both the case of correlated metal with the bandwidth $W\ensuremath{\lesssim}U$ and that of doped Mott insulator with
U⪢W (
U---the value of local Hubbard interaction). The optical conductivity calculated within $\mathrm{DMFT}+{\ensuremath{\sum}}_{\mathbf{p}}$ demonstrates typical pseudogap behavior within the quasiparticle band, in qualitative agreement with experiments in copper oxide superconductors. For large values of
U, pseudogap anomalies are effectively suppressed.
We investigate the interplay between the formation of a lattice and magnetic polaron in the case of a single hole in the antiferromagnetic background. We present an exact analytical solution of the Holstein $t\ensuremath{-}J$ model in infinite dimensions. The ground-state energy, electron-lattice correlation function, spin bag dimension as well as spectral properties are calculated. The magnetic and hole-lattice correlations sustain each other, i.e., the presence of antiferromagnetic correlations favors the formation of the lattice polaron at lower values of the electron-phonon coupling while the polaronic effect contributes to reduce the number of spin defects in the antiferromagnetic background. The crossover towards a spin-lattice small polaron region of the phase diagram becomes a discontinuous transition in the adiabatic limit.