Exploring unconventional quantum criticality in the p-wave-paired Aubry-Andr\'{e}-Harper model

• URL: http://arxiv.org/abs/2210.06740v1
• Date: Thu, 13 Oct 2022 05:10:43 GMT
• Title: Exploring unconventional quantum criticality in the p-wave-paired Aubry-Andr\'{e}-Harper model
• Authors: Ting Lv, Yu-Bin Liu, Tian-Cheng Yi, Liangsheng Li, Maoxin Liu, and Wen-Long You
• Abstract summary: We investigate scaling properties near the quantum critical point in the Aubry-Andr'e-Harper model with p-wave pairing. We find that the spectrum averaged entanglement entropy and the generalized fidelity susceptibility act as eminent universal order parameters of the corresponding critical point.
• Score: 0.5937476291232802
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We have investigated scaling properties near the quantum critical point between the extended phase and the critical phase in the Aubry-Andr\'{e}-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 sizes increase in the Fibonacci sequence. The retrieved values of $\nu \simeq 1.000$ and $z \simeq 3.610$ 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.

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