Prof. Martin Mosquera, Montana State University, "Theory of Extended Bose-Hubbard Systems and Two-Dimensional Materials"

Ultracold Atomic Lattices are promising systems for quantum simulation and quantum computation. The Bose-Hubbard model continues to be fundamental for the development and testing of new theories that can be used to study Rydberg atom clusters and lattices. Using the hard-core boson version of this model, we discuss recent work in formulating unitary coupled cluster theory for general time-dependent domains and particle correlation regimes of medium (to possibly high) strength, with opportunities for the accurate computation of quantum observables and time-correlation functions (with some present limitations noted). For the second part of the talk we consider Two-Dimensional Materials, which are also promising for a wide variety of optoelectronic applications in quantum and semiconductor technologies. My group has worked in recent years on using machine learning, band structure theory, and parameter-free quantum modeling to investigate multiferroic phenomena, twistronics, and exciton functionalities. We discuss progress in these directions where we show that machine-learned potentials are effective in describing phonon transport and structural defects, and where band theory is reliable for supporting and explaining the experimental modulation of excitons in twisted transition-metal dichalcogenide bilayers.