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Exactly solvable Hamiltonian model of the doubled Ising and $mathbb{Z}_2$ toric code topological phases separated by a gapped domain wall via anyon condensation | | Yu Zhao
; Shan Huang
; Hongyu Wang
; Yuting Hu
; Yidun Wan
; | | Date: |
26 Sep 2022 | | Abstract: | In this paper, we construct an exactly lattice Hamiltonian model of two
topological phases separated by a gapped domain wall via anyon condensation. To
be specific, we study the properties of this model in the case of the doubled
Ising phase and $mathbb{Z}_2$ toric code phase with a gapped domain wall in
between. Our model is a concrete spatial counterpart of the phase transition
triggered by anyon condensation, in the sense that the algebraically understood
phenomena, such as splitting, identification, and confinement, in anyon
condensation can be manifested in the spatial wavefunctions of our model. Our
model also helps generalize the characteristic properties of a single
topological phase: We find that the ground state degeneracy of two topological
phases separated by two gapped domain walls on the torus is equal to the number
of quasiparticle types in the gapped domain walls; we also find the $S$ and $T$
matrices of our model. | | Source: | arXiv, 2209.12750 | | Services: | Forum | Review | PDF | Favorites | |
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