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

Abstract

We investigate the quantum criticality and universality in Aubry-André-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 $\varphi =\pi$ alleviates the odd-even effect of scaling functions across the Aubry-André 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 $\varphi$. A thorough numerical analysis with odd number of system sizes reveals the correlation-length exponent $\nu \simeq 1.000$ and the dynamical exponent $z$ $\simeq$ 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-André transition. The results may be testified in near term state-of-the-art experimental settings.

12 pages, 7 figures, accepted by Physical Review A

References in corpus (25)

• Anderson Transitions
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Many-Body Localization in a Quasiperiodic System
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
• Observation of a quantum phase transition in the quantum Rabi model with a single trapped ion
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit
• Adiabatic quantum dynamics of a random Ising chain across its quantum critical point
• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• Phase transitions in a non-Hermitian Aubry-André-Harper model
• Exact many-body scars and their stability in constrained quantum chains
• Fidelity approach to the disordered quantum XY model
• On the Area Law for Disordered Free Fermions
• Generalized Aubry-André-Harper model with p-wave superconducting pairing
• Fidelity Susceptibility in One-dimensional Disordered Lattice Models
• Fidelity, fidelity susceptibility and von Neumann entropy to characterize the phase diagram of an extended Harper model
• Generalized fidelity susceptibility at phase transitions
• Fidelity Susceptibility in the Quantum Rabi Model
• Dynamics of a quantum phase transition in the Aubry-André-Harper model with $p$-wave superconductivity
• Many-body localization in the interpolating Aubry-André-Fibonacci model
• Inverse participation ratios in the XXZ spin chain
• Signatures of metal-insulator and topological phase transitions in the entanglement of one-dimensional disordered fermions
• Phase diagram of a generalized off-diagonal Aubry-André model with p-wave pairing

Cited by in corpus (4)

• Fidelity susceptibility as a diagnostic of the commensurate-incommensurate transition: A revisit of the programmable Rydberg chain
• Exploring unconventional quantum criticality in the p-wave-paired Aubry-André-Harper model
• Quantum criticality of a ${\mathbb{Z}}_3$ symmetric spin chain with long-range interactions
• Long-Range Order and Quantum Criticality in Antiferromagnetic Chains with Long-Range Staggered Interactions