Conformal Field Theories generated by Chern Insulators under Quantum Decoherence

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 Z = tr{ρ_c^D ρ^Ω} is mapped to the partition function of the desired CFT, where ρ_c^D and ρ^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 Z is mapped to the partition function of the U(2N)₁ CFT; under weak decoherence, the Chern insulator density matrix can experience certain instability, and the “partition function” Z can flow to other interacting CFTs with smaller central charges. The Renyi relative entropy F = − log tr{ρ_c^D ρ^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 F, analogous to the well-known finite size scaling of 2d CFT.