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Characteristic Properties and Domain-Wall Verlinde Formula of Composite Topological Systems via Anyon Condensation in Exactly Solvable Models

12/25 2023 Seminar
  • Title Characteristic Properties and Domain-Wall Verlinde Formula of Composite Topological Systems via Anyon Condensation in Exactly Solvable Models
  • Speaker Yu Zhao(Fudan Univ.)
  • Date 10:30-11:30 Dec. 25, 2023
  • Venue 6620
    • Abstract
     We partially apply anyon condensation to half of an exactly solvable lattice model describing a topological phase, resulting in an exactly solvable model of a composite topological system. This system consists of the original topological phase and the child SET phase post anyon condensation, separated by a gapped domain wall. We investigate the characteristic properties of this composite topological system. By examining the ground-state degeneracy of such a composite system on a torus, we find it matches the number of domain-wall excitation types, as well as the interdomain excitation types, as these two sets of excitations label two bases of the ground states. The basis transformation, represented by the domain-wall S matrix, serving as the characteristic property of this composite system, encodes the braiding between interdomain and domain-wall excitations. Additionally, we derive the domain-wall Verlinde Formulae, which utilizes the domain-wall S matrix to determine the fusion rules of interdomain excitations, which are revealed to be fractional or irrational values. This fractionalization or irrationalization phenomenon stems from ungauging during anyon condensation.
    References:
    [1] Yu Zhao, Shan Huang, Hongyu Wang, Yuting Hu, Yidun Wan, SciPost Phys. Core 6, 076 (2023).
    [2] Yu Zhao, Hongyu Wang, Yuting Hu, Yidun Wan, arXiv:2304.08475 (2023).

    Inviter:
    Hao Song