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

TL;DR

This paper investigates the quantum criticality in a p-wave paired Aubry-Andre9-Harper model, revealing universal scaling behavior and critical exponents that differ from traditional localization transitions, with implications for quantum simulations.

Contribution

It introduces a unified scaling theory for the critical point between extended and critical phases in a quasiperiodic system with p-wave pairing, identifying new universality class features.

Findings

Spectral entanglement entropy and fidelity susceptibility serve as universal order parameters.

Critical exponents nd z are estimated as .999 and .610.

Transition belongs to a different universality class from localization transitions.

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.