Transport and dynamical properties of electron-phonon coupled systems

by David Jansen
Cumulative thesis
Date of Examination:2022-12-06
Date of issue:2023-01-31
Advisor:Prof. Dr. Fabian Heidrich-Meisner
Referee:Prof. Dr. Fabian Heidrich-Meisner
Referee:Prof. Dr. Stefan Kehrein
Persistent Address: http://dx.doi.org/10.53846/goediss-9675

 

 

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Abstract

English

In this thesis, I investigate the transport and dynamical properties of electron-phonon coupled systems using numerical methods. I focus on the one-dimensional Holstein model, which incorporates both polaron and charge density wave (CDW) physics, and use matrix-product-state-based algorithms. In the first part, I present work where we combine purification with local basis optimization to study the finite-temperature properties of the model. This gives access to polaron spectral functions, polaron and bipolaron optical conductivity, and the energy-transport coefficient at finite filling. The second part focuses on the Holstein model coupled to two tight-binding leads. There, we investigate how current is transported through the structure and how CDW states break down. In the last part, we analyze the spread of an electron in a lattice and the decay of CDWs. We aim to understand if a full quantum mechanical treatment of the phonons is necessary or if trajectory-based algorithms are applicable.
Keywords: Theoretical physics; Solid-state physics; Many-body systems; Holstein model; Electron-phonon systems; Matrix-product states; DMRG; Polarons; Bipolarons; Local basis optimization; Charge density waves
 
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