This thesis investigates ultracold molecules as a resource for novel quantum many-body physics, in particular by utilizing their rich internal structure and strong, long-range dipole-dipole interactions. In addition, numerical methods based on matrix product states are analyzed in detail, and general algorithms for investigating the static and dynamic properties of essentially arbitrary one-dimensional quantum many-body systems are put forth. Finally, this thesis covers open-source implementations of matrix product state algorithms, as well as educational material designed to aid in the use of understanding such methods.

Auteur
Michael Wall performed research for his thesis at the Colorado School of Mines, USA. He has since received the Nicholas Metropolis award for outstanding doctoral thesis work in computational physics and is currently a postdoctoral fellow at NIST NRC.

Contenu

Part I: Introduction.- General Introduction.- Models for Strongly Correlated Lattice Physics.- Part II: The Molecular Hubbard Hamiltonian.- Emergent Timescales in Entangled Quantum Dynamics of Ultracold Molecules in Optical Lattices.- Hyperfine Molecular Hubbard Hamiltonian.- Part III: The Fermi Resonance Hamiltonian.- Microscopic Model for Feshbach Interacting Fermions in an Optical Lattice with Arbitrary Scattering Length and Resonance Width.- Part IV: Matrix Product States.- Matrix Product States: Foundations.- Out-of-Equilibrium Dynamics with Matrix Product States.- The Infinite Size Variational Matrix Product State Algorithm.- Finite Temperature Matrix Product State Algorithms and Applications.- Part V: Open Source Code and Educational Materials.- Open Source Code Development.- Educational Materials.- Part VI: Conclusions and Appendices.- Conclusions and Suggestions for Future Research.- Appendix A: Documentation for ALPS V2.0 TEBD Code.- Appendix B: Educational Materials: A Gentle Introduction to Time Evolving Block Decimation (TEBD).- Appendix C: Educational Materials: Introduction to MPS Algorithms.