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Institute for Condensed Matter Theory Seminar: Rank-2 toric code and dipolar braiding statistics

Event Type
The Institute for Condensed Matter Theory
190 ESB
Dec 5, 2022   12:00 pm  
Jung Hoon Han, Sungkyunkwan University
Janice Benner
Originating Calendar
Physics - Institute for Condensed Matter Theory Seminar

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. If time permits, I will discuss recent progress in constructing the tensor-network wave function of the R2TC ground state and understanding its topological entanglement entropy. 

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