David Jansen (Georg-August-Universität Göttingen)
DMRG methods for dynamical properties of electron-phonon systems at finite temperatures

We compute the optical conductivity for the Holstein polaron and bipolaron with dispersive phonons at finite temperature using a matrix-product state-based method [1]. We combine purification [2], to obtain the finite-temperature states [3], together with the parallel time-dependent variational principle (pTDVP) [4] algorithm to compute the real-time current-current correlation functions. The pTDVP algorithm utilizes local basis optimization [5] to efficiently treat the phononic degrees of freedom. For the polaron, we find that the phonon dispersion alters the optical conductivity at several temperatures in the weak, intermediate, and strong coupling regimes. In the first two cases, we see that the spectrum goes from being continuous to discrete when going from an upwards to a downwards phonon dispersion relation. In the strong coupling regime, the dispersion leads to a shift of the center of the spectrum. For the bipolaron, we also see that the dispersion shifts the spectrum. The results fit well with an analytical expression derived from the Born-Oppenheimer Hamiltonian. 

[1] Jansen et al., arXiv:2206.00985 (2022)
[2] Verstraete et al., Phys. Rev. Lett. 93, 207204 (2004)
[3] Jansen et al., Phys. Rev. B 102, 165155 (2020)
[4] Secular et al., Phys. Rev. B 101, 235123 (2020) 
[5] Zhang et al., Phys. Rev. Lett. 80, 2661 (1998)