Conformal Field Theories generated by Chern Insulators under Quantum Decoherence
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914650975633408 |
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| author | Su, Kaixiang Myerson-Jain, Nayan Xu, Cenke |
| author_facet | Su, Kaixiang Myerson-Jain, Nayan Xu, Cenke |
| contents | We demonstrate that the fidelity between a pure state trivial insulator and the mixed state density matrix of a Chern insulator under decoherence can be mapped to a variety of two-dimensional conformal field theories (CFT); more specifically, the quantity $\mathcal{Z} = \text{tr}\{ \hatρ^D_c \hatρ_Ω\}$ is mapped to the partition function of the desired CFT, where $\hatρ^D_c$ and $\hatρ_Ω$ are respectively the density matrices of the decohered Chern insulator and a pure state trivial insulator. For a pure state Chern insulator with Chern number $2N$, the fidelity $\mathcal{Z}$ is mapped to the partition function of the $\text{U}(2N)_1$ CFT; under weak decoherence, the Chern insulator density matrix can experience certain instability, and the "partition function" $\mathcal{Z}$ can flow to other interacting CFTs with smaller central charges. The Rényi relative entropy $\mathcal{F} = - \log \text{tr}\{ \hatρ^D_c \hatρ_Ω\}$ is mapped to the free energy of the CFT, and we demonstrate that the central charge of the CFT can be extracted from the finite size scaling of $\mathcal{F}$, analogous to the well-known finite size scaling of $2d$ CFT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_13410 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Conformal Field Theories generated by Chern Insulators under Quantum Decoherence Su, Kaixiang Myerson-Jain, Nayan Xu, Cenke Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics We demonstrate that the fidelity between a pure state trivial insulator and the mixed state density matrix of a Chern insulator under decoherence can be mapped to a variety of two-dimensional conformal field theories (CFT); more specifically, the quantity $\mathcal{Z} = \text{tr}\{ \hatρ^D_c \hatρ_Ω\}$ is mapped to the partition function of the desired CFT, where $\hatρ^D_c$ and $\hatρ_Ω$ are respectively the density matrices of the decohered Chern insulator and a pure state trivial insulator. For a pure state Chern insulator with Chern number $2N$, the fidelity $\mathcal{Z}$ is mapped to the partition function of the $\text{U}(2N)_1$ CFT; under weak decoherence, the Chern insulator density matrix can experience certain instability, and the "partition function" $\mathcal{Z}$ can flow to other interacting CFTs with smaller central charges. The Rényi relative entropy $\mathcal{F} = - \log \text{tr}\{ \hatρ^D_c \hatρ_Ω\}$ is mapped to the free energy of the CFT, and we demonstrate that the central charge of the CFT can be extracted from the finite size scaling of $\mathcal{F}$, analogous to the well-known finite size scaling of $2d$ CFT. |
| title | Conformal Field Theories generated by Chern Insulators under Quantum Decoherence |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2305.13410 |