Correction to: Communications Physics https://doi.org/10.1038/s42005-020-00484-1, published online 27 November 2020.

It was brought to the authors’ attention that equation [1] in our originally published article was first derived in Rumpf, B. Simple statistical explanation for the localization of energy in nonlinear lattices with two conserved quantities. Phys. Rev. E 69, 016618 (2004) [34] as equation [9], in the same form when \(\kappa\) in [1] is set to unity, \(K\) in [9] is set to 0 and \({{{\mathscr{P}}}}\), \(U\) and \(M\) in [1] corresponds to \({A}_{ < }\), \({E}_{ < }\) and \(N\) in [9], respectively. In ref. [34], this equation was introduced to describe the small fluctuation entropy of a defocusing discrete nonlinear Schrödinger equation. To acknowledge this early result, a corresponding change has been made after Eq. [1] in our manuscript, and reference [34] has been added to the main original article.

The following correction have been made:

On page 4, after equation (1), the following text has been added: “It was first derived in ref. [34] in order to account for the small fluctuation entropy of the defocusing nonlinear Schrödinger equation.”

Reference [34], Rumpf, B. Simple statistical explanation for the localization of energy in nonlinear lattices with two conserved quantities. Phys. Rev. E 69, 016618, https://doi.org/10.1103/PhysRevE.69.016618, was added to the reference list.

The correction has been applied to both the HTML and PDF version of the article.