Imaginary-field-driven phase transition for the 2D Ising antiferromagnet: A fidelity-susceptibility approach

The square-lattice Ising antiferromagnet subjected to the imaginary magnetic field H=iθT∕2 with the “topological” angle θ and temperature T was investigated by means of the transfer-matrix method. Here, as a probe to detect the order–disorder phase transition, we adopt an extended version of the fidelity susceptibility χ_F ^(θ), which makes sense even for such a non-hermitian transfer matrix. As a preliminary survey, for an intermediate value of θ, we examined the finite-size-scaling behavior of χ_F ^(θ), and found a pronounced signature for the criticality; note that the magnetic susceptibility exhibits a weak (logarithmic) singularity at the Néel temperature. Thereby, we turn to the analysis of the power-law singularity of the phase boundary at θ=π. With θ−π scaled properly, the χ_F ^(θ) data are cast into the crossover scaling formula, indicating that the phase boundary is shaped concavely. Such a feature makes a marked contrast to that of the mean-field theory.