1:00–2:00 pm
Please Join us:
Carolyn Zhang’s PhD Thesis Defense
EXACTLY SOLVABLE MODELS: QUANTUM CRITICALITY, DYNAMICS, AND TOPOLOGY
This thesis is a collection of three short stories on the applications of simple toy models in different topics in condensed matter theory. In the first two stories, we present new toy models that provide a refined understanding of complex physical phenomena by distilling them down to their minimal ingredients. In the third story, which is the focus of this talk, we prove limitations of a broad class of toy models known as commuting projector Hamiltonians. These models, which include the celebrated toric code model, have been powerful tools for studying interacting topological phases of matter. We use a flux insertion argument to prove that a commuting projector Hamiltonian cannot realize a phase with a nonzero electric Hall conductance. In particular, it cannot realize the integer quantum Hall effect, the prototypical example of a topological phase of matter.
Committee Members:
Michael Levin (Chair)
Cheng Chin
Clay Córdova
Dam T. Son
Carolyn will be a Junior Fellow at the Harvard Society of Fellows.