Universal algebraic growth of entanglement entropy in many-body localized systems with power-law interactions

TL;DR

This paper demonstrates that in disordered systems with power-law interactions, the entanglement entropy grows algebraically with a universal exponent at the many-body localization transition, revealing fundamental insights into localization phenomena.

Contribution

The study uncovers a universal entanglement growth exponent at the MBL transition across various models and links it to the critical decay power of interactions.

Findings

Universal entanglement growth exponent $oxed{ ext{~}0.33}$ at MBL transition

Consistent exponent across different lattice models and decay powers

Relation between $oxed{ ext{exponent } ext{and} ext{decay power}}$ of interactions

Abstract

Power-law interactions play a key role in a large variety of physical systems. In the presence of disorder, these systems may undergo many-body localization for a sufficiently large disorder. Within the many-body localized phase the system presents in time an algebraic growth of entanglement entropy, $S_{vN}(t)\propto t^{\gamma}$. Whereas the critical disorder for many-body localization depends on the system parameters, we find by extensive numerical calculations that the exponent $\gamma$ acquires a universal value $\gamma_c\simeq 0.33$ at the many-body localization transition, for different lattice models and decay powers. Moreover, our results suggest an intriguing relation between $\gamma_c$ and the critical minimal decay power of interactions necessary for the observation of many-body localization.