Effective Conformal Field Theory generated from Pure and Dephased Chern insulator

Abstract

We demonstrate that the fidelity between two states with different Chern numbers $\mathcal{Z}=\mathrm{tr}\{\rho {\rho }^{\prime }\}$ serves as a generating theory for an effective conformal field theory (CFT) at the $(2+0)d$ temporal interface. $\rho$ can be chosen as a pure trivial insulator, and ${\rho }^{\prime }$ can be taken as a pure or dephased Chern insulator density matrix. More specifically, we obtain the following results: (1) through evaluation of the effective central charge, stiffness, and correlation function (the ``strange correlators"), we demonstrate that the fidelity between a trivial insulator and an insulator with Chern number $C=1$ maps to a CFT with effective central charge $c_{\mathrm{eff}}=1$; while the fidelity between two Chern insulators with Chern numbers $C=\pm 1$ maps to a CFT with $c_{\mathrm{eff}}=2$. (2) The density matrix of the Chern insulator becomes a quantum spin Hall insulator in the doubled Hilbert space, and the dephasing acts as interaction between the two spin species. (3) In the limit of infinite dephasing the Chern insulator becomes a superconductor in the doubled Hilbert space, featuring the ``strong-weak" U(1) spontaneous symmetry breaking. The analysis based on Laughlin wave function and previous studies of projected wave function of quantum spin Hall insulator suggest this is a power-law superconductor. (4) With increasing strength of dephasing, the amplitude of single particle strange correlator is suppressed, while the Cooper pair strange correlator is enhanced, consistent with the trend of emerging superconductivity.

References in corpus (23)

• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Quantum criticality under decoherence or weak measurement
• Topology of density matrices
• Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements
• Long-range entanglement from measuring symmetry-protected topological phases
• Topological indices for open and thermal systems via Uhlmann's phase
• Diagnostics of mixed-state topological order and breakdown of quantum memory
• Measurements conspire nonlocally to restructure critical quantum states
• Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States
• Symmetry protected topological phases under decoherence
• Pivot Hamiltonians as generators of symmetry and entanglement
• Entanglement in one-dimensional critical state after measurements
• Characterizing the Haldane phase in quasi-one-dimensional spin-1 Heisenberg antiferromagnets
• Measurement-altered Ising quantum criticality
• Channeling quantum criticality
• Unifying Emergent Hydrodynamics and Lindbladian Low Energy Spectra across Symmetries, Constraints, and Long-Range Interactions
• Topological Phases with Average Symmetries: the Decohered, the Disordered, and the Intrinsic
• Symmetry-enforced many-body separability transitions
• Strange correlations in spin-1 Heisenberg antiferromagnets
• Hidden order and flux attachment in symmetry protected topological phases: a Laughlin-like approach
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Conformal Field Theories generated by Chern Insulators under Quantum Decoherence
• Spin Liquid and Superconductivity emerging from Steady States and Measurements

Cited by in corpus (1)

• Phase Transition of Topological Index driven by Dephasing