Towards a Qubit-Lattice Model of the E_8 State
This event is part of the Biophysics/Condensed Matter Seminar Series.
For decades an important goal of condensed matter physics has been to classify and understand all possible phases of matter, and the phase transitions between them. Quantum physics allows for interesting new phases, called topological phases. It is generally believed that, in two dimensions, we can classify all topological phases of matter at an abstract level, but we have no intuitive handle on the vast majority of these. In particular, the "E8 state" is an interesting two-dimensional topological phase of matter which is known to exist, but which is difficult to understand and work with. I conjecture a simple model for the E8 state based on a lattice of qubits coupled with a local Hamiltonian. While I have not proved this model is in the E_8 phase, I have intermediate results which are important in their own right. These include the construction of models achieving various simpler phases and a study of the edges of some simple phases as they undergo a phase transition.