Fig. 5: The numerical results of the generic double semion wavefunction.
From: Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions
The correlation length ξ for different bond dimensions D along the a hx = 0.5 cut and b hx-axis, where hx and hz are two tuning magnetic field parameters. c The free energy \(f=-\mathrm{log}\,(| {\lambda }_{0}| )\) (red line) from the leading eigenvalue λ0 and the arguments \(\arg ({\lambda }_{j})\) (blue lines) of three dominant eigenvalues λj of the transfer matrix operator along the circle h = 0.85, where h is the loop tension and θ is the spin angle. d The finite scaling of the entanglement entropy S versus the correlation length ξ at the point (hx, hz) = (0.5, −0.8) inside the dense loop phase. The blue line is \(S=({c}_{* }/6)\mathrm{log}\,\xi +{S}_{0}\) with the estimated effective central charge c* ≈ 2.00, where S0 is a non-universal constant. The red dots are the numerical data. e At the point (hx, hz) = (0.500, −0.470) on the phase transition line CF in the phase diagram Fig. 4b between the double semion phase and the dense loop phase, the estimated effective central charge is c* ≈ 1.01.
