Conformal Field Theories generated by Chern Insulators under Quantum Decoherence

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 $\mathcal{Z}=\text{tr}\{{\hat{\rho }}_c^D{\hat{\rho }}_{\Omega }\}$ is mapped to the partition function of the desired CFT, where ${\hat{\rho }}_c^D$ 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 Rényi relative entropy $\mathcal{F}=-\log \text{tr}\{{\hat{\rho }}_c^D{\hat{\rho }}_{\Omega }\}$ 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.

arXiv comment8.5 pages, including references

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• Decoherence through Ancilla Anyon Reservoirs
• Mixed-State Topological Order under Coherent Noise
• Quantum Strong-to-Weak Spontaneous Symmetry Breaking in Decohered One Dimensional Critical States
• Relaxation Critical Dynamics in Measurement-induced Phase Transitions
• Effective Conformal Field Theory generated from Pure and Dephased Chern insulator