Kai-Hsin Wu - U(1) symmetry enriched toric code

  • Starts: 12:00 pm on Wednesday, November 29, 2023
  • Ends: 4:30 pm on Wednesday, November 29, 2023
In this presentation, we propose and study a generalization of Kitaev's Z2 toric code with an additional global U(1) symmetry. We will begin by introducing the system defined on a ladder geometry. This ladder system can be understood analytically through mapping to dual models. We then shift our focus to investigate the system on a 2D square lattice. Using quantum Monte Carlo simulation, we find strong evidence for a topologically ordered ground state manifold with indications of UV-IR mixing, i.e., the topological degeneracy of the ground state depends on the microscopic details of the lattice. Specifically, the ground state degeneracy depends on the lattice tilt relative to the directions of the torus cycles. In particular, we observe that while the usual compactification along the vertical or horizontal lines of the square lattice shows a twofold ground state degeneracy, compactifying the lattice at 45∘ leads to a threefold degeneracy. In addition to its unusual topological properties, this system also exhibits Hilbert space fragmentation, as well as translational symmetry breaking.
CDS 365
Kai-Hsin Wu
Boston University
Claudio Chamon