Physics Theory Seminar with Kaden Hazzard on Quantum Matter
Understanding quantum many-body systems is a major goal across physics, but we often must resort to severe approximations. Exact results, though rare, give powerful insights. I will describe our progress on two fronts: rigorous bounds on observables, and new exactly solvable models.
The bounds I describe are manifestations of locality. For example, when only nearby objects can interact, correlations spread only in a "light-cone" with finite speed (Lieb-Robinson bounds). I will first describe a method that gives infinitely tighter light-cone speeds for large spins and other important situations, and which enables important applications, such as useful bounds on finite-size error in numerical simulations. I will also describe our proof of the profound principle that (for gapped ground states) "local perturbations perturb locally" in power law interacting systems, enabled by ideas that connect nonequilibrium and equilibrium phenomena.
I will also describe our recent construction of an exactly solvable model that displays parastatistical excitations, particles that are neither fermions or bosons. Moreover, unlike anyons, they can be created in three dimensions. This provides a rich new family of possible quasiparticles in condensed matter, as well as potential candidates for fundamental particles. Remarkably, these theories naturally arise in arrays of ultracold molecules or Rydberg atoms.