Exploring unconventional quantum criticality in the p -wave-paired Aubry-André-Harper model

We have investigated scaling properties near the quantum critical point between the extended phase and the critical phase in the Aubry-Andre-Harper model with p-wave pairing, which have rarely been exploited as most investigations focus on the localization transition from the critical phase to the localized phase. We find that the spectrum-averaged entanglement entropy and the generalized fidelity susceptibility act as eminent universal order parameters of the corresponding critical point without gap closing. We introduce a Widom scaling Ansatz for these criticality probes to develop a unified theory of critical exponents and scaling functions. We thus extract the correlation-length critical exponent nu and the dynamical exponent z through the finite-size scaling given the system size increase in the Fibonacci sequence. The retrieved values of nu similar or equal to 1.000 and z similar or equal to 3.610 indicate that the transition from the extended phase to the critical phase belongs to a different universality class from the localization transition. Our approach sets the stage for exploring the unconventional quantum criticality and the associated universal information of quasiperiodic systems in state-of-the-art quantum simulation experiments.