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The notion of fidelity susceptibility, introduced within the context of quantum metric tensor, has been an important quantity to characterize the criticality near quantum phase transitions. We demonstrate that for topological phase transitions in Dirac models, provided the momentum space is treated as the manifold of the quantum metric, the fidelity susceptibility coincides with the curvature function whose integration gives the topological invariant. Thus the quantum criticality of the curvature function near a topological phase transition also describes the criticality of the fidelity susceptibility, and the correlation length extracted from the curvature function also gives a momentum scale over which the fidelity susceptibility decays. To map out the profile and criticality of the fidelity susceptibility, we turn to quantum walks that simulate one-dimensional class BDI and two-dimensional class D Dirac models, and demonstrate their accuracy in capturing the critical exponents and scaling laws near topological phase transitions.
We analyze ground-state behaviors of fidelity susceptibility (FS) and show that the FS has its own distinct dimension instead of real systems dimension in general quantum phases. The scaling relation of the FS in quantum phase transitions (QPTs) is t
We study the quantum fidelity approach to characterize thermal phase transitions. Specifically, we focus on the mixed-state fidelity induced by a perturbation in temperature. We consider the behavior of fidelity in two types of second-order thermal p
Motivated by recent development in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshkov-Glick model. We get the fidelity
We investigate the Loschmidt amplitude and dynamical quantum phase transitions in multiband one dimensional topological insulators. For this purpose we introduce a new solvable multiband model based on the Su-Schrieffer-Heeger model, generalized to u
The extension of the notion of quantum fidelity from the state-space level to the operator one can be used to study environment-induced decoherence. state-dependent operator fidelity sucepti- bility (OFS), the leading order term for slightly differen