Quantum criticality of generalized Aubry-Andr\'{e} models with exact mobility edges using fidelity susceptibility

TL;DR

This paper investigates quantum critical phenomena in generalized Aubry-Andre9 models using fidelity susceptibility to identify mobility edges and analyze critical exponents, revealing universal properties of quasiperiodic systems.

Contribution

It introduces a novel application of fidelity susceptibility to determine mobility edges and critical exponents in generalized Aubry-Andre9 models, linking to Fibonacci sequences and universality classes.

Findings

Successfully identifies mobility edges using fidelity susceptibility.

Determines critical exponents and universality class for the model.

Demonstrates the method's effectiveness in analyzing quantum criticality.

Abstract

In this study, we explore the quantum critical phenomena in generalized Aubry-Andr\'{e} models, with a particular focus on the scaling behavior at various filling states. Our approach involves using quantum fidelity susceptibility to precisely identify the mobility edges in these systems. Through a finite-size scaling analysis of the fidelity susceptibility, we are able to determine both the correlation-length critical exponent and the dynamical critical exponent at the critical point of the generalized Aubry-Andr\'{e} model. Based on the Diophantine equation conjecture, we can determines the number of subsequences of the Fibonacci sequence and the corresponding scaling functions for a specific filling fraction, as well as the universality class. Our findings demonstrate the effectiveness of employing the generalized fidelity susceptibility for the analysis of unconventional quantum criticality and the associated universal information of quasiperiodic systems in cutting-edge quantum simulation experiments.