Operator fidelity susceptibility: An indicator of quantum criticality

We introduce an operator fidelity and propose to use its susceptibility for characterizing the sensitivity of quantum systems to perturbations. Two typical models are addressed: One is the transverse Ising model exhibiting a quantum phase transition, and the other is the one-dimensional Heisenberg spin chain with next-nearest-neighbor interactions, which has the degeneracy. It is revealed that the operator fidelity susceptibility is a good indicator of quantum criticality regardless of the system degeneracy.

Figure 1

Partial derivative of the fidelity susceptibility versus the parameter $\lambda$ for different system sizes $N=2^{10},2^{11},2^{12}$. The inset plots the fidelity susceptibility ${\chi }_F$ versus the parameter $\lambda$. The time $t=100$.

Figure 2

(a) The operator fidelity susceptibility versus $J_2$ for different system sizes $N=7,9,11$. (b) The mixed state fidelity susceptibility versus $J_2$.