We apply the Dynamical Mean Field Theory to calculate the low-density limit of the optical conductivity in the Holstein model. This non perturbative treatment allows to span continuously from the weak-coupling quasi-free electron behaviour to the strong-coupling small polaron picture. New features arise in the intermediate coupling regime: i) a noticeable transfer of spectral weight towards low frequencies occurs at low temperatures, when coherent processes acquire importance; ii) thermally activated Polaron Interband Transitions appear at non zero temperature, whose spectral weight has a non monotonic temperature behaviour. We propose an interpretation of the infrared active vibrations (IRAV) observed in the optical spectra of the underdoped superconducting cuprates in terms of small polarons in the intermediate coupling regime.
A comprehensive picture of polaron and bipolaron physics is essential to understand the optical absorption spectrum in many materials with electron-phonon interactions. In particular, the finite-temperature properties are of interest since they play an important role in many experiments. Here, we combine the parallel two-site time-dependent variational principle algorithm (p2TDVP) with local basis optimization (LBO) and purification to calculate time-dependent current-current correlation functions. From this information, we extract the optical conductivity for the Holstein polaron and bipolaron with dispersive phonons at finite temperatures. For the polaron in the weak and intermediate electron-phonon coupling regimes, we analyze the influence of phonon dispersion relations on the spectra. For strong electron-phonon coupling, the known result of an asymmetric Gaussian is reproduced for a flat phonon band. For a finite phonon bandwidth, the center of the Gaussian is either shifted to larger or smaller frequencies, depending on the sign of the phonon hopping. We illustrate that this can be well understood by considering the Born-Oppenheimer surfaces. Similar behavior is seen for the bipolaron for strong coupling. For the bipolaron with weak and intermediate coupling strengths and a flat phonon band, we obtain two very different spectra. The latter also has a temperature-dependent resonance at a frequency below the phonon frequency.
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.
We compute the Holstein polaron spectral function on a one-dimensional ring using the finite-temperature
T Lanczos method. With increasing
T additional features in the spectral function emerge even at temperatures below the phonon frequency. We observe a substantial spread of the spectral weight towards lower frequencies and the broadening of the quasiparticle (QP) peak. In the weak-coupling regime the QP peak merges with the continuum in the high-
T limit. In the strong-coupling regime the main features of the low-
T spectral function remain detectable up to the highest
T used in our calculations. The effective polaron mass shows a nonmonotonic behavior as a function of
T at small phonon frequency but increases with
T at larger frequencies. The self-energy remains
k independent even at elevated
T in the frequency range corresponding to the polaron band, while at higher frequencies it develops a distinguishable
k dependence. Analytical expressions for the first few frequency moments are derived, and they agree well with those extracted from numerical calculations in a wide-
T regime.