Ground states, symmetries and dynamics of quantum many-body lattice systems
This project proposes a study of ground state phases of quantum lattice systems. The problem of detecting and describing quantum ground state phase transitions is a fundamental problem in the theory of quantum computing, where quantum information is stored in the ground state space of a many-body interaction. This study focuses on three avenues of research. The first is to investigate the stability of spectral gaps and the existence of symmetric invariants in 2D quantum spin systems. Such a program has already been carried out in frustration free models with local topological quantum order such as models with projected entangled pair ground states, but there remain important and open questions in more general models. The second direction is to study applications of quasi-adiabatic continuation methods to quantum lattice systems with unbounded Hamiltonians. These results would extend known results be applicable to models such as the quantum rotor and yield information about the adiabatic theorem in previously unknown cases. Lastly, the study focuses on propagation velocities and quasi-locality of many-body quantum dynamics.