| Abstract: | We study the localization problem of one-dimensional interacting spinless fermions in anincommensurate optical lattice, which changes from an extended phase to a non-ergoicmany-body localized phase by increasing the strength of the incommensurate potential. Weidentify that there exists an intermediate regime before the system enters the many-bodylocalized phase, in which both the localized and extended many-body states coexist, thusthe system is divided into three different phases, which can be characterized bynormalized participation ratios of the many-body eigenstates and distributions of naturalorbitals of the corresponding one-particle density matrix. This is very different from itsnoninteracting limit, in which all eigenstates undergo a delocalization-localizationtransition when the strength of the incommensurate potential exceeds a critical value. |
