IMSc Webinar

The shift invariant and a new Hofstadter butterfly

Naren Manjunath,

Department of Physics, Condensed Matter Theory Center, and Joint Quantum Institute, The University of Maryland, College Park, Maryland

The 'shift' is a universal property of certain gapped topological
phases of matter, such as the quantum Hall states. It encodes how certain
ground state properties depend on the curvature of the underlying spatial
manifold (for example, a sphere versus a torus). The notion of shift can be
defined for continuum as well as lattice systems in (2+1) dimensions. In
this ongoing work, we numerically obtain the shift in the Hofstadter model
of free fermions on a square lattice with a uniform magnetic field. We do
this in two ways, by computing (i) the charge bound to disclination defects
on the square lattice; (ii) the rotation eigenvalue of the ground state
with an additional uniformly inserted magnetic flux. We find that the shift
forms a 'Hofstadter butterfly' with seemingly fractal properties. Our work
provides an additional characterization of the square lattice Hofstadter
model apart from the usual Hall conductivity, and also suggests a route
towards a complete characterization.

Collaborators: Yuxuan Zhang, Gautam Nambiar, and Maissam Barkeshli (UMCP)

Here is the link to the Google meet:
meet.google.com/ujh-dswt-bso