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Fusion of Low-Entanglement Excitations in 2D Toric Code
by Jing-Yu Zhao, Xie Chen
Submission summary
| Authors (as registered SciPost users): | Xie Chen · Jingyu Zhao |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2409.07544v1 (pdf) |
| Date submitted: | 2024-10-02 05:33 |
| Submitted by: | Zhao, Jingyu |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
On top of a $D$-dimensional gapped bulk state, Low Entanglement Excitations (LEE) on $d$($<D$)-dimensional sub-manifolds can have extensive energy but preserves the entanglement area law of the ground state. Due to their multi-dimensional nature, the LEEs embody a higher-category structure in quantum systems. They are the ground state of a modified Hamiltonian and hence capture the notions of `defects' of generalized symmetries. In previous works, we studied the low-entanglement excitations in a trivial phase as well as those in invertible phases. We find that LEEs in these phases have the same structure as lower-dimensional gapped phases and their defects within. In this paper, we study the LEEs inside non-invertible topological phases. We focus on the simple example of $\mathbb{Z}_2$ toric code and discuss how the fusion result of 1d LEEs with 0d morphisms can depend on both the choice of fusion circuit and the ordering of the fused defects.
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