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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 towards 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, chi_p, chi_D and chi_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 = 0.241J1 between a gapless Heisenberg phase for J2 < J2_critical and a dimerized phase for J2 > J2_critical. This phase transition, in the Berezinskii-Kosterlitz-Thouless universality class, is controlled by a marginal operator and is therefore particularly difficult to observe.