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Monday, January 23, 2023 at 12:00pm
Clark Hall, 701 Central Campus, 142 Sciences Drive
Jung Hoon Han
Professor, Department of Physics
Rank-2 toric code and dipolar braiding statistics
A rank-2 toric code (R2TC) Hamiltonian in two dimensions has been constructed as a Higgsed descendant of rank-2 U(1) lattice gauge theory. The quasiparticles in R2TC exhibit what I call the ‘dipolar braiding statistics’ rather than the well-known ‘monopolar braiding statistics’ of mutual anyons. Within the flux attachment picture, the statistical phase captures the total dipole moment, not the total charge, of the anyons encompassed in the braiding process. Pertinent U(1) field theories of the quasiparticles’ dynamics as well as their dipolar braiding statistics are developed, leading to the ‘dipolar BF action’ of the rank-2 gauge fields. Ground state degeneracy exhibits sensitivity on the linear system size vs. N - the local Hilbert space dimension - and varies from N^3 to N^6. I will discuss recent progress in understanding R2TC as originating from two copies of rank-1 theories through a certain condensation process and show that this view permits also the construction of the exact wave function for the ground state of R2TC as two copies of R1TC ground state wave functions that are sewn together by some isometry operation. The R2TC wave function can then be used to discuss its topological entanglement entropy features.