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

Abstract

We have investigated scaling properties near the quantum critical point between the extended phase and the critical phase in the Aubry-André-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.

arXiv comment14 pages, 8 figures, accepted by Physical Review B

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Cited by in corpus (11)

• Renormalization-Group Theory of 1D quasiperiodic lattice models with commensurate approximants
• Quantum criticality and Kibble-Zurek scaling in the Aubry-André-Stark model
• Identifying non-Hermitian critical points with quantum metric
• Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
• Quantum criticality of generalized Aubry-André models with exact mobility edges using fidelity susceptibility
• Unveiling quantum criticality of disordered Aubry-André-Harper models via typical fidelity susceptibility
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Superconducting properties of Fibonacci chains with enhanced superconducting pairing at the boundaries
• Generalized Aubry-André-Harper model with power-law quasiperiodic potentials
• Critical properties in the non-Hermitian Aubry-Andre-Stark model
• Arithmetic Tuning of Dynamical Critical Exponents in Quasiperiodic Localization Transitions