Abstract: I will discuss two topics that I have been collaborating on in CMTC. The first involves a careful study of an analog of the chiral anomaly in one dimension that was motivated by work from the Galitski group at Maryland which showed that the response of the chiral charge to electromagnetic fields could be affected by interactions. At the same time, the chiral anomaly, when it arises at boundaries of topological phases, is known to be associated with topological terms that cannot be renormalized. I will discuss explicit calculation of various response functions of one dimensional interacting systems that show that while interactions can affect the current response, which is the variable used in relativistic as well as topological field theories to define the chiral charge, it does not affect the momentum response. The momentum response has been proposed in condensed matter anomalies by Lieb/Schulz/Mattis. The anomalous current response is shown to be related to a conserved chiral charge in a weakly gapped Sine-Gordon model.
In a second part of my talk, I will discuss work in progress towards a nearly analytical model for a classical time-crystal that builds on the period doubling transition of a driven Harmonic oscillator. We will analyze a limit of a weakly non-linear damped version of the system where the spontaneous breaking of time-translation symmetry can be described as a conventional symmetry breaking transition using a Landau free-energy. Both topics are works in progress, and the talk is intended to motivate discussion and collaboration.
Location: ATL 4402