The Holstein model is the simplest model that describes an electron that propagates through the crystal and interacts with local optical phonons. We will present the spectral functions and (frequency dependent) 

mobility for a broad range of parameters, obtained using several approximate and numerically “exact” methods.  First, we will show that the dynamical mean field theory provides an excellent, numerically cheap, approximate solution for the spectral function of the Holstein model in the whole range of parameters, even in one dimension. We will analytically   show that the vertex corrections to conductivity vanish in the weak coupling limit. For stronger electron-phonon coupling the frequency-dependent mobility in one dimension is calculated using the hierarchical equations of motion method and dynamical quantum typicality. The impact of the vertex corrections is the strongest near the adiabatic limit, where we make comparison with phenomenological transient localization theory which is often used for a description of charge transport in molecular organic semiconductors. Finally, we will discuss the applicability of the quantum-classical approach for calculation of charge transport.

1) P. Mitric, V. Jankovic, N. Vukmirovic, and D. Tanaskovic, “Spectral Functions of the Holstein Polaron: Exact and Approximate Solutions”, Phys. Rev. Lett. 129, 096401 (2022).

2) V. Jankovic, P. Mitric, D. Tanaskovic, and N. Vukmirovic: “Vertex Corrections to Conductivity in the Holstein Model: a Numerical-Analytical Study” Phys. Rev. B 109, 214312 (2024).

3) P. Mitric, V. Dobrosavljevic, and D. Tanaskovic: “Precursors to Anderson Localization in the Holstein Model: Quantum and Quantum-classical Solutions” Phys. Rev. B 111, L161105 (2025).

4) P. Mitric, Dynamical Quantum Typicality: Simple Method for Investigating Transport Properties Applied to the Holstein Model, Phys. Rev. B 111, 195140 (2025).

Join Zoom Meeting:

https://us06web.zoom.us/j/5081440931

Meeting ID: 508 144 0931

Seminar hosts: Neven Šantić i Matija Čulo