Calendar

I’ll tell a mathematical story that runs from Archimedes’ hat-box theorem of ~200BC (which he used to calculate the surface area of the sphere), to the properties of “Porter-Thomas” probability distributions, all the way to my and others’ work establishing the theoretical foundations of Google’s quantum supremacy experiment from this past fall.  While this admittedly has little to do with mathematical picture languages, there will be pictures of spheres.

via Zoom: https://harvard.zoom.us/j/779283357

I will describe a construction of gapped 3D lattice models with non-Abelian fractons from gauging subsystem symmetries of topological layers. I will describe how this relates to previously constructed fracton models with nonabelian particles and explain how our construction fits into the recently developed picture of gapped fracton phases as topological defect networks.

via Zoom Video Conferencing:  https://harvard.zoom.us/s/977347126

*note special time: 1:30 – 3:00 pm Eastern

A Van Hove singularity (VHS) of the density of states (DOS) is universal in a periodic system.  In two dimensions, a saddle point of energy dispersion yields a logarithmic divergence in the DOS.  Here, we introduce a new kind of VHS, motivated by the recent development of moiré materials.  We define a high-order VHS, which gives a power-law DOS divergence [1].  It requires only a single tuning parameter, such as a twist angle of a moiré material, pressure, and strain.  We further perform a renormalization group analysis near a high-order VHS to study the effect of electron interactions [2].  We reveal a nontrivial metallic state, where various divergent susceptibilities coexist, but no long-range order appears.  We call such a metallic state as a supermetal.  Our controlled analysis shows that a supermetal at the interacting fixed point is a non-Fermi liquid.

[1] N. F. Q. Yuan, H. Isobe, and L. Fu, Nat. Commun. 10, 5769 (2019).
[2] H. Isobe and L. Fu, Phys. Rev. Research 1, 033206 (2019).

via Zoom: https://harvard.zoom.us/j/977347126