Fidelity-susceptibility analysis of the honeycomb-lattice Ising antiferromagnet under the imaginary magnetic field

The honeycomb-lattice Ising antiferromagnet subjected to the imaginary magnetic field H = i theta T/2 with the topological angle theta and temperature T was investigated numerically. In order to treat such a complex-valued statistical weight, we employed the transfer-matrix method. As a probe to detect the order-disorder phase transition, we resort to an extended version of the fidelity F, which makes sense even for such a non-Hermitian transfer matrix. As a preliminary survey, for an intermediate value of theta, we investigated the phase transition via the fidelity susceptibility chi ((theta))(F). The fidelity susceptibility chi ((theta))(F) exhibits a notable signature for the criticality as compared to the ordinary quantifiers such as the magnetic susceptibility. Thereby, we analyze the end-point singularity of the order-disorder phase boundary at theta = . We cast the chi ((theta))(F) data into the crossover-scaling formula with delta theta = - theta scaled carefully. Our result for the crossover exponent phi seems to differ from the mean-field and square-lattice values, suggesting that the lattice structure renders subtle influences as to the multi-criticality at theta = pi