Conformal Field Theories generated by Chern Insulators under Quantum Decoherence

• URL: http://arxiv.org/abs/2305.13410v1
• Date: Mon, 22 May 2023 18:50:35 GMT
• Title: Conformal Field Theories generated by Chern Insulators under Quantum Decoherence
• Authors: Kaixiang Su, Nayan Myerson-Jain, Cenke Xu
• Abstract summary: 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) We demonstrate that the central charge of the CFT can be extracted from the finite size scaling of $mathcalF$, analogous to the well-known finite size scaling of $2d$ CFT.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $\mathcal{Z} = \text{tr}\{ \hat{\rho}^D_c \hat{\rho}_\Omega \}$ is mapped to the partition function of the desired CFT, where $\hat{\rho}^D_c$ and $\hat{\rho}_\Omega$ 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 R\'{e}nyi relative entropy $\mathcal{F} = - \log \text{tr}\{ \hat{\rho}^D_c \hat{\rho}_\Omega \}$ 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.

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