Localization of interacting Fermi gases in quasiperiodic potentials

TL;DR

This study explores how weak interactions influence the metal-insulator transition in a one-dimensional Fermi gas within a quasiperiodic potential, revealing that repulsive interactions tend to promote metallic behavior by shifting the critical transition point.

Contribution

It provides the first unbiased quantum Monte Carlo analysis of the many-body localization transition in a quasiperiodic Fermi gas, highlighting the linear shift of the critical point due to interactions.

Findings

Weak repulsive interactions shift the critical potential strength for localization.

Quantum Monte Carlo accurately identifies the metal-insulator transition.

Interactions favor metallic behavior by enlarging the delocalized phase.

Abstract

We investigate the zero-temperature metal-insulator transition in a one-dimensional two-component Fermi gas in the presence of a quasi-periodic potential resulting from the superposition of two optical lattices of equal intensity but incommensurate periods. A mobility edge separating (low energy) Anderson localized and (high energy) extended single-particle states appears in this continuous-space model beyond a critical intensity of the quasi-periodic potential. In order to discern the metallic phase from the insulating phase in the interacting many-fermion system, we employ unbiased quantum Monte Carlo (QMC) simulations combined with the many-particle localization length familiar from the modern theory of the insulating state. In the noninteracting limit, the critical optical-lattice intensity for the metal-insulator transition predicted by the QMC simulations coincides with the Anderson localization transition of the single-particle eigenstates. We show that weak repulsive interactions induce a shift of this critical point towards larger intensities, meaning that repulsion favors metallic behavior. This shift appears to be linear in the interaction parameter, suggesting that even infinitesimal interactions can affect the position of the critical point.