Finite lattice techniques for strongly interacting many body systems

Dean Lee

Shainen M. Davidson

Understanding the collective behaviour of many-body quantum systems is an important subject in many areas of physics. With advances in ultra-cold gas experiments, the dynamics of strongly-interacting systems can now be studied in the lab. However, there is a paucity of theoretical techniques available to simulate such systems. One technique is phase-space methods, often known as the Truncated Wigner Approximation; however, its applicability in its naive form is limited. In this work, we expound on techniques to expand the regimes in which it can be effective. This involves creating a novel phase-space that is tailored to the problem at hand, and associated classical equations of motion. We show techniques for lattice systems with local finite Hilbert spaces, for fermionic systems, and for many-body localized systems. In all cases, we benchmark the accuracy of the approximation against exact results.

R. F. Bishop, Yang Xian

Jianzhong Zheng

This thesis addresses the question of a strongly interacting many-body problem: the Hubbard model on one- and two-dimensional lattices. The technique employed is the small-cluster method wherein the full many-body Hamiltonian for finite clusters with periodic boundary conditions (PBC's) is solved exactly. We first apply this technique to an extended one-dimensional chain and a two-dimensional square-lattice Hubbard model. We then construct a two-dimensional overlayer/substrate Hubbard model with first- and second-nearest-neighbor hopping, on-site and nearest-neighbor interactions, and overlayer-site orbital energy. The ground-state properties are investigated and discussed in a many-body picture.

C. Binegar, Jared Austin, Samuel E. Begg +3 more

We present the experimental detection of coherent three-body interactions, often masked by stronger two-body effects, through nonequilibrium spin dynamics induced by controllably quenching lattice-confined spinor gases. Three-body interactions are characterized through both real-time and frequency domain analyses of the observed dynamics. Our results, well-described by an extended Bose-Hubbard model, further demonstrate the importance of three-body interactions for correctly determining atom distributions in lattice systems, which has applications in quantum sensing via spin singlets. The techniques demonstrated in this work can be directly applied to other atomic species, offering a promising avenue for future studies of higher-body interactions with broad relevance to strongly-interacting quantum systems.

Dean Lee