Longitudinal-field fidelity susceptibility analysis of the 𝐽1-𝐽2 transverse-field Ising model around 𝐽2∕𝐽1 ≈ 0.5

The square-lattice 𝐽1-𝐽2 transverse-field (TF) Ising model was investigated with the exact diagonalization (ED) method. In order to analyze the TF-driven phase transition, we applied the longitudinal-field fidelity susceptibility 𝜒(ℎ)𝐹, which is readily evaluated via the ED scheme. Here, the longitudinal field couples with the absolute value of the magnetic moment |𝑀| rather than the raw 𝑀 so that the remedied fidelity susceptibility exhibits a peak around the critical point; note that the spontaneous magnetization does not appear for the finite-size systems. As a preliminary survey, the modified fidelity susceptibility 𝜒(ℎ)𝐹 is applied to the analysis of criticality for 𝐽2 = 0, where a number of preceding results are available. Thereby, properly scaling the distance from the multi-criticality, 𝜂 = 0.5−𝐽2, the 𝜒(ℎ)𝐹 data were cast into the crossover-scaling formula, and the multi-critical exponent for 𝜒(ℎ)𝐹 is estimated. The result is cross-checked by the numerically evaluated 𝛽-function behavior.