Tensor Network Representations for Intrinsically Mixed-State Topological Orders
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908473304809472 |
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| author | Aldossari, Bader Blinov, Sergey Luo, Zhu-Xi |
| author_facet | Aldossari, Bader Blinov, Sergey Luo, Zhu-Xi |
| contents | Tensor networks are an efficient platform to represent interesting quantum states of matter as well as to compute physical observables and information-theoretic quantities. We present a general protocol to construct fixed-point tensor network representations for intrinsically mixed-state topological phases, which exhibit nontrivial topological phenomena and do not have pure-state counterparts. The method exploits the power of anyon condensation in Choi states and is applicable to the cases where the target states arise from pure-state topological phases subject to strong decoherence/disorders in the Abelian sectors. Representative examples include $m^a e^b$ decoherence of $\mathbb{Z}_N$ toric code, decohered non-Abelian $S_3$ quantum double as well as pure $Z$/$X$ decoherence of arbitrary CSS codes. An example of chiral topological phases which cannot arise from local commuting projector models are also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22989 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor Network Representations for Intrinsically Mixed-State Topological Orders Aldossari, Bader Blinov, Sergey Luo, Zhu-Xi Strongly Correlated Electrons Mathematical Physics Quantum Physics Tensor networks are an efficient platform to represent interesting quantum states of matter as well as to compute physical observables and information-theoretic quantities. We present a general protocol to construct fixed-point tensor network representations for intrinsically mixed-state topological phases, which exhibit nontrivial topological phenomena and do not have pure-state counterparts. The method exploits the power of anyon condensation in Choi states and is applicable to the cases where the target states arise from pure-state topological phases subject to strong decoherence/disorders in the Abelian sectors. Representative examples include $m^a e^b$ decoherence of $\mathbb{Z}_N$ toric code, decohered non-Abelian $S_3$ quantum double as well as pure $Z$/$X$ decoherence of arbitrary CSS codes. An example of chiral topological phases which cannot arise from local commuting projector models are also presented. |
| title | Tensor Network Representations for Intrinsically Mixed-State Topological Orders |
| topic | Strongly Correlated Electrons Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2507.22989 |