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 $H=i\theta T\mathrm{/}2$ 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 ${\chi }_F^{(\theta )}$. The fidelity susceptibility ${\chi }_F^{(\theta )}$ 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 $\theta =\pi$. We cast the ${\chi }_F^{(\theta )}$ data into the crossover-scaling formula with $\delta \theta = \pi-\theta$scaledcarefully\mathrm{.}Ourresultforthecrossoverexponent$\phi$ 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 $\theta =\pi$.