IQIM Postdoctoral and Graduate Student Seminar

Abstract: Gapped lattice Hamiltonians often exhibit topological properties at low energy, described by topological quantum field theory. However, this connection is difficult to make precise. Part of the difficulty is that not all gapped systems actually behave this way, with fractons providing a counterexample. I discuss some local conditions on the ground state or Hamiltonian that guarantee topological properties. These conditions distinguish ordinary topological phases from systems like fractons, offering a candidate definition for a genuine topological phase. With such definitions in hand, we can attempt to classify these phases. I describe some past and ongoing progress with Isaac Kim (arXiv:2405.17379), Alexei Kitaev, and Milo Moses.

Lunch will be provided on the lawn outside the Bridge building, following the talk.