General quantum fidelity susceptibilities for the J1-J2 chain

We study slightly generalized quantum fidelity susceptibilities where the differential change in the fidelity is measured with respect to a different term than the one used for driving the system toward a quantum phase transition. As a model system we use the spin-1/2 J₁-J₂ antiferromagnetic Heisenberg chain. For this model, we study three fidelity susceptibilities, χ_ρ, χ_D, and χ_AF, which are related to the spin stiffness, the dimer order, and antiferromagnetic order, respectively. All these ground-state fidelity susceptibilities are sensitive to the phase diagram of the J₁-J₂ model. We show that they all can accurately identify a quantum critical point in this model occurring at J₂^c∼0.241J₁ between a gapless Heisenberg phase for J₂<J₂^c and a dimerized phase for J₂>J₂^c. This phase transition, in the Berezinskii-Kosterlitz-Thouless universality class, is controlled by a marginal operator and is therefore particularly difficult to observe.