Non-power-law universal scaling in incommensurate systems

TL;DR

This paper reveals a universal, alpha-independent non-power-law scaling in incommensurate systems, demonstrated through superfluid and heat capacity measurements, challenging prior beliefs about alpha sensitivity.

Contribution

It introduces a universal non-power-law scaling law in incommensurate systems, independent of the irrational parameter alpha, across different physical models.

Findings

Universal alpha-independent scaling law discovered

Scaling characterized by t ~ r^{ζ log log r}

Confirmed in Bose and Fermi gas systems

Abstract

Previous studies of incommensurate systems concluded that critical scaling in such systems is sensitively dependent on the irrational, $\alpha$, which determines the incommensuration. Contrary to this belief, in the canonical Harper-Hofstadter model, we show there is universal $\alpha$-independent scaling for almost all $\alpha$. This critical scaling is characterized by non-power law time-length scaling $t \sim r^{\zeta \log \log r}$. We demonstrate this in the superfluid fraction of a Bose gas, and the heat capacity of a Fermi gas. We argue that this scaling is generic of a broad class of incommensurate models.