Testing the universality of the many-body metal-insulator transition by time evolution of a disordered one-dimensional ultracold fermionic gas

TL;DR

This study uses tDMRG to explore how disorder and interactions influence the metal-insulator transition in a 1D ultracold fermionic gas, revealing that the transition's properties depend on interaction strength and are not universal.

Contribution

It demonstrates the non-universality of the 1D metal-insulator transition by analyzing the time evolution across different interaction regimes using scaling and theoretical arguments.

Findings

Transition depends on interaction strength

Anomalous diffusion characterizes the transition

Strong interactions lead to ballistic motion

Abstract

It is now possible to study experimentally the combined effect of disorder and interactions in cold atom physics. Motivated by these developments we investigate the dynamics around the metal-insulator transition (MIT) in a one-dimensional (1D) Fermi gas with short-range interactions in a quasiperiodic potential by the time-dependent density-matrix renormalization group (tDMRG) technique. By tuning disorder and interactions we study the MIT from the weakly to the strongly interacting limit. The MIT is not universal as time evolution, well described by a process of anomalous diffusion, depends qualitatively on the interaction strength. By using scaling ideas we relate the parameter that controls the diffusion process with the critical exponent that describes the divergence of the localization length. In the limit of strong interactions theoretical arguments suggest that the motion at the MIT tends to ballistic and critical exponents approach mean-field predictions.