Longitudinal-field fidelity susceptibility analysis of the $J_1$-$J_2$ transverse-field Ising model around $J_2/J_1\approx 0.5$

Abstract

The square-lattice $J_1$-$J_2$ 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 ${\chi }_F^{(h)}$, 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 ${\chi }_F^{(h)}$ is applied to the analysis of criticality for $J_2=0$, where a number of preceding results are available. Thereby, properly scaling the distance from the multi-criticality, $\eta =0.5-J_2$, the ${\chi }_F^{(h)}$ data were cast into the crossover-scaling formula, and the multi-critical exponent for ${\chi }_F^{(h)}$ is estimated. The result is cross-checked by the numerically evaluated $\beta$-function behavior.

References in corpus (21)

• Ground state overlap and quantum phase transitions
• Decay of Loschmidt Echo Enhanced by Quantum Criticality
• Dynamics of Loschmidt echoes and fidelity decay
• Computational Studies of Quantum Spin Systems
• Quantum Critical Scaling of Fidelity Susceptibility
• Quantum phase transition dynamics in the two-dimensional transverse-field Ising model
• Critical behavior at m-axial Lifshitz points: field-theory analysis and $\epsilon$-expansion results
• Two-loop renormalization-group analysis of critical behavior at m-axial Lifshitz points
• The critical Binder cumulant in a two--dimensional anisotropic Ising model with competing interaction
• Ground-state fidelity at first-order quantum transitions
• Quantum Ising model on the frustrated square lattice
• Genuine Multipartite Entanglement in the Cluster-Ising Model
• Emergence of string-valence bond solid state in the frustrated $J_1-J_2$ transverse field Ising model on the square lattice
• Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models
• Quantum phase diagram of two-dimensional transverse field Ising model: unconstrained tree tensor network and mapping analysis
• Qualitative aspects of the phase diagram of J1-J2 model on the cubic lattice
• Criticalities of the transverse- and longitudinal-field fidelity susceptibilities for the d=2 quantum Ising model
• Extended scaling for ferromagnetic Ising models with zero-temperature transitions
• Multicritical behavior of the fidelity susceptibility for the 2D quantum transverse-field $XY$ model
• Critical behavior of the fidelity susceptibility for the d=2 transverse-field Ising model
• Primary and Secondary Order Parameters in the Fully Frustrated Transverse Field Ising Model on the Square Lattice