Resonance-induced growth of number entropy in strongly disordered systems

TL;DR

This paper investigates the growth of number entropy in strongly disordered, many-body localized systems, revealing that observed slow growth is compatible with localization and can be explained by resonance effects.

Contribution

The study introduces an analytical model accounting for resonances that explains the observed number entropy growth in disordered systems, reconciling numerical results with localization.

Findings

Number entropy shows trivial initial growth and slow power-law increase.

Resonance effects explain the variability in entropy growth across disorder realizations.

Saturation value of number entropy scales with disorder strength.

Abstract

We study the growth of the number entropy $S_N$ in one-dimensional number-conserving interacting systems with strong disorder, which are believed to display many-body localization. Recently a slow and small growth of $S_N$ has been numerically reported, which, if holding at asymptotically long times in the thermodynamic limit, would imply ergodicity and therefore the absence of true localization. By numerically studying $S_N$ in the disordered isotropic Heisenberg model we first reconfirm that, indeed, there is a small growth of $S_N$. However, we show that such growth is fully compatible with localization. To be specific, using a simple model that accounts for expected rare resonances we can analytically predict several main features of numerically obtained $S_N$: trivial initial growth at short times, a slow power-law growth at intermediate times, and the scaling of the saturation value of $S_N$ with the disorder strength. Because resonances crucially depend on individual disorder realizations, the growth of $S_N$ also heavily varies depending on the initial state, and therefore $S_N$ and von Neumann entropy can behave rather differently.