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arXiv · 2209.12750

Characteristic Properties of a Composite System of Topological Phases Separated by Gapped Domain Walls via an Exactly Solvable Hamiltonian Model

Yu Zhao·Shan Huang·Hongyu Wang·Yuting Hu·Yidun Wan
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Abstract

In this paper, we construct an exactly solvable lattice Hamiltonian model to investigate the properties of a composite system consisting of multiple topological orders separated by gapped domain walls. There are interdomain elementary excitations labeled by a pair of anyons in different domains of this system; This system also has elementary excitations with quasiparticles in the gapped domain wall. Each set of elementary excitations corresponds to a basis of the ground states of this composite system on the torus, reflecting that the ground-state degeneracy matches the number of either set of elementary excitations. The characteristic properties of this composite system lie in the basis transformations, represented by the $S$ and $T$ matrices: The $S$ matrix encodes the mutual statistics between interdomain excitations and domain-wall quasiparticles, and the $T$ matrix encapsulates the topological spins of interdomain excitations. Our model realizes a spatial counterpart of a temporal phase transition triggered by anyon condensation, bringing the abstract theory of anyon condensation into manifestable spatial interdomain excitation states.

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Yu Zhao, Shan Huang, Hongyu Wang, Yuting Hu, Yidun Wan. 2023-06-24. Characteristic Properties of a Composite System of Topological Phases Separated by Gapped Domain Walls via an Exactly Solvable Hamiltonian Model. https://doi.org/10.21468/scipostphyscore.6.4.076

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