Quantum thermodynamics explorations with a Hubbard-Holstein dimer

Sammanfattning: The goal of this project is to characterize the quantum thermodynamics of a Hubbard-Holstein dimer. We explore how the standard formalism of quantum thermodynamics behaves in the context many-body physics. To this end, the simplest possible lattice model which includes electron and electron-phonon interactions is used, namely the Hubbard-Holstein dimer. The system is time evolved using exact diagonalization, the Suzuki-Trotter method and the Lanczos method. We prepare various parts of the system in an initial thermal bath. We then compare the work to a case that does not include phonons. Three thermodynamic cases are realized: a battery, a few paths in phase space and a thermodynamic cycle. The results show that the effect of phonons is to smoothen out the features in the work distribution. We have seen that the battery can be charged, by increasing the amount of phonons. The path in phase space showed a path dependence, as we expected from classical thermodynamics. Finally, we have seen that the cycle experiences irreversibility by exhibiting hysteresis.