Mathematical Physics Seminar: Free Parafermions and More

Final PhD seminar

schedule Date & time
23 Mar 2023 | 11:15am - 12pm
person Speaker


Robert Henry, ANU
contact_support Contact
Murray Batchelor

Content navigation



In this PhD completion talk I describe the free parafermion model, which is a one-dimensional discrete quantum system built on Zn-symmetric clock states, which generalises the Ising spin chain. This model has a special exact solution generalising free fermions. The model is non-Hermitian, which gives it a complex spectrum and other unusual behaviour, but is also PT-symmetric, which can serve as an analog of Hermiticity and allows a definition of unitary time evolution. In this talk, I report on a newly-discovered series of exceptional points where the Jordan structure of the Hamiltonian becomes non-trivial. These exceptional points accumulate near the critical point and explain some of the model's unusual behaviour. Some other results are also described including a new free parafermionic model constructed with different generalised operators, some results about the free parafermion model with periodic boundaries (which is surprisingly nontrivial), and a determination of the phase diagram of a staggered Heisenberg XX model using Majorana zero modes.

Join Zoom Meeting

Meeting ID: 872 8790 7198

Password: 095570


Online via Zoom