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

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 finitetemperature 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.

Metallicity in the Dissipative Hubbard-Holstein Model: Markovian and Non-Markovian Tensor-Network Methods for Open Quantum Many-Body Systems

“…The description of bosonic degrees of freedom has posed substantial challenges to MPS methods because of their infinite-dimensional Hilbert spaces. Much work has been devoted to an accurate and efficient truncation of bosonic Hilbert spaces, resulting in successful techniques such as the pseudo site (PS) method [24] and the local-basis optimization (LBO) method [19,[114][115][116][117]. In this context, a newly-introduced MPS method is the so-called projected purification [97].…”

“…This is mainly due to the extremely high numerical costs for simulating phononic degrees of freedom, whose local Hilbert spaces are, in principle, infinitedimensional. The computational limitations become even more severe when incorporating more realistic foundations for anharmonicities, such as treating the phononic system as an open quantum system (OQS) or considering dispersive behavior [18,19]. The past decades have also seen a rapid development of highly efficient numerical tools, enabling simulations of a large number of quantum mechanical degrees of freedom.…”