Quantum criticality and universality in the p-wave-paired Aubry-Andre-Harper model

We investigate the quantum criticality and universality in Aubry-Andre-Harper (AAH) model with p-wave superconducting pairing Delta in terms of the generalized fidelity susceptibility (GFS). We show that the higher order GFS is more efficient in spotlighting the critical points than lower order ones, and thus the enhanced sensitivity is propitious for extracting the associated universal information from the finite-size scaling in quasiperiodic systems. The GFS obeys power-law scaling for localization transitions and thus scaling properties of the GFS provide compelling values of critical exponents. Specifically, we demonstrate that the fixed modulation phase phi = pi alleviates the odd-even effect of scaling functions across the Aubry-Andre transition with Delta = 0, while the scaling functions for odd and even numbers of system sizes with a finite Delta cannot coincide irrespective of the value of phi. A thorough numerical analysis with odd number of system sizes reveals the correlation-length exponent upsilon similar or equal to 1.000 and the dynamical exponent z similar or equal to 1.388 for transitions from the critical phase to the localized phase, suggesting the unusual universality class of localization transitions in the AAH model with a finite p-wave superconducting pairing lies in a different universality class from the Aubry-Andre transition. The results may be testified in near term state-of-the-art experimental settings.

Automated summary

We investigate the quantum criticality and universality in the Aubry-Andre-Harper (AAH) model with p-wave superconducting pairing, Delta, using the generalized fidelity susceptibility (GFS). We find that higher order GFS is more effective in identifying critical points and extracting universal information through finite-size scaling. The GFS exhibits power-law scaling for localization transitions, providing compelling values of critical exponents. Our analysis demonstrates that a fixed modulation phase alleviates the odd-even effect in scaling functions across the Aubry-Andre transition with Delta = 0, while scaling functions for odd and even system sizes with a finite Delta cannot coincide regardless of the value of the phase. Numerical analysis reveals specific correlation-length and dynamical exponents for transitions from the critical phase to the localized phase, suggesting a different universality class for localization transitions in the AAH model with finite p-wave superconducting pairing compared to the Aubry-Andre transition. These results can potentially be verified in near-term experimental settings.