Parameterized Families of Toric Code Phase: $em$-duality family and higher-order anyon pumping
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913091278602240 |
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| author | Ohyama, Shuhei Ando, Takamasa Thorngren, Ryan |
| author_facet | Ohyama, Shuhei Ando, Takamasa Thorngren, Ryan |
| contents | Within the toric-code phase, we study parameterized families of topologically ordered states. We construct $1$- and $2$-parameter families of local Hamiltonians and confirm their non-triviality via topological pumping. For the $1$-parameter family, we show that the $em$-exchange defect is pumped into the bond Hilbert space of a tensor-network representation. For the $2$-parameter case, we construct a ``pump of a pump'' that transports an $S^1$-family of a system in one lower spatial dimension. Using similar methods, we also present a $1$-parameter family with a higher-order anyon pump that produces corner-localized anyon modes. These constructions provide explicit lattice realizations and concrete diagnostics of family-level topology. We use recently developed boundary algebra methods to study the non-triviality of these families. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03891 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parameterized Families of Toric Code Phase: $em$-duality family and higher-order anyon pumping Ohyama, Shuhei Ando, Takamasa Thorngren, Ryan Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Quantum Physics Within the toric-code phase, we study parameterized families of topologically ordered states. We construct $1$- and $2$-parameter families of local Hamiltonians and confirm their non-triviality via topological pumping. For the $1$-parameter family, we show that the $em$-exchange defect is pumped into the bond Hilbert space of a tensor-network representation. For the $2$-parameter case, we construct a ``pump of a pump'' that transports an $S^1$-family of a system in one lower spatial dimension. Using similar methods, we also present a $1$-parameter family with a higher-order anyon pump that produces corner-localized anyon modes. These constructions provide explicit lattice realizations and concrete diagnostics of family-level topology. We use recently developed boundary algebra methods to study the non-triviality of these families. |
| title | Parameterized Families of Toric Code Phase: $em$-duality family and higher-order anyon pumping |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2605.03891 |