Stark many-body localization

TL;DR

This paper demonstrates that spinless fermions in a strong electric field exhibit many-body localization-like behavior, with localized wave functions and slow entanglement growth, even without disorder.

Contribution

It shows that Wannier-Stark localization persists with interactions, revealing a form of many-body localization in a disorder-free system.

Findings

Entanglement entropy grows logarithmically with time after a quench.

Level statistics are Poissonian, indicating localization.

Predicted experimental signatures similar to disorder-induced MBL.

Abstract

We consider spinless fermions on a finite one-dimensional lattice, interacting via nearest-neighbor repulsion and subject to a strong electric field. In the non-interacting case, due to Wannier-Stark localization, the single-particle wave functions are exponentially localized even though the model has no quenched disorder. We show that this system remains localized in the presence of interactions and exhibits physics analogous to models of conventional many-body localization (MBL). In particular, the entanglement entropy grows logarithmically with time after a quench, albeit with a slightly different functional form from the MBL case, and the level statistics of the many-body energy spectrum are Poissonian. We moreover predict that a quench experiment starting from a charge-density wave state would show results similar to those of Schreiber et al. [Science 349, 842 (2015)].