Abstract

The wide controllability of the physical parameters in cold atoms have made it possible to experimentally investigate various concepts in quantum many-body physics. Identifying and understanding the many-body phases in the strongly correlated regime have been a challenge both for theorists and experimentalists. The real-time dynamics of such systems have been observed experimentally and is expected to provide better understanding of the phase structure. Even in one-dimensional systems where many powerful theoretical methods exist, the effect of interparticle interaction on the localization of bosonic atoms in disordered potential remains controversial. Here we study a related problem of the interacting spin-1/2 fermions in a lattice with the site energy modified by a quasiperiodic potential, which works as a disorder. The density-matrix renormalization group (DMRG) method allows numerically exact study of the ground state properties of one-dimensional lattice systems of interacting atoms. We find that a short-range attractive interaction induces localization [1]. By the time-dependent DMRG , we also study the real-time evolution of the system close to the “metal”-insulator transition after a trap potential is removed while the quasiperiodic potential is kept on. We analyze the critical exponents of the diffusion process and compare the results against the non-interacting cases and the mean-field predictions [2].

[1] M. Tezuka and A. M. Garcia-Garcia: Phys. Rev. A 82, 043613 (2010). [2] A. M. Garcia-Garcia and M. Tezuka: in preparation.