Full Description
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.
Contents
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.
