Determine the dynamical critical exponent for generalized Fibonacci modulations with m greater than one

Determine the dynamical critical exponent z for generalized Fibonacci quasiperiodic modulations with m>1 by overcoming the strong finite-size effects that prevent reliable energy-gap scaling and data collapse, potentially using larger systems and more accurate rational approximants.

Background

The paper studies the Aubry–André–Harper model with quasiperiodic onsite potentials whose irrational modulation frequencies are generated by generalized Fibonacci recursions. For the m=1 family, the authors extract the dynamical critical exponent z from both fourth-order generalized fidelity susceptibility and finite-size energy-gap scaling, finding that z varies with the arithmetic structure of the irrational frequency.

For cases with m>1, the localization-length analysis supports the correlation-length exponent ν=1, but the energy-gap data do not yield a satisfactory finite-size collapse. Consequently, the dynamical exponent remains unresolved for this part of the parameter family. The authors suggest that larger systems and more accurate rational approximants may be necessary to resolve the issue.