Finite-temperature optical conductivity with density-matrix renormalization group methods for the Holstein polaron and bipolaron with dispersive phonons

TL;DR

This paper develops a computational approach combining advanced algorithms to calculate the finite-temperature optical conductivity of Holstein polarons and bipolarons with dispersive phonons, revealing how phonon dispersion affects spectral features.

Contribution

It introduces a novel method combining p2TDVP, LBO, and purification to compute finite-temperature optical spectra for electron-phonon systems with dispersive phonons.

Findings

Phonon dispersion shifts the Gaussian peak in spectra depending on phonon hopping sign.

Strong coupling spectra show asymmetric Gaussian behavior consistent with flat phonon bands.

Weak/intermediate bipolaron spectra exhibit distinct features and temperature-dependent resonances.

Abstract

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. A 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.