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We study localization and many-body localization transition in onedimensional systems in the presence of deterministic quasi-periodic potentials.We focus on single-particle excitations obtained through single-particleGreen's function in real space. A single parameter scaling analysis of theratio of the typical to average value of the local density of states (LDOS) ofsingle particle excitations shows that the critical exponent with which thecorrelation length $\xi$ diverges at the transition point $\xi \sim|h-h_c|^{-\nu}$, coming from the localized side, satisfies the inequality $\nu\ge 1$ for the non-interacting Aubry-Andre (AA) model as well as for thedeterministic aperodic model studied here. For the interacting systems, westudy single particle excitations produced in highly excited many-bodyeigenstates across the MBL transition and found that the critical exponentobtained from finite-size scaling of the ratio of the typical to average valueof the LDOS satisfies $\nu \ge 1$ here as well. This analysis of local densityof states shows that the localization and MBL transition in systems withquasi-periodic potentials belong to a different universality class than thelocalization and MBL transition in systems with random disorder where $\nu \ge2$. This is in complete contrast to the level spacing ratio which is known tosupport the same universality class for MBL transitions in systems withquasiperiodic as well as random disorder potentials. For the interactingsystems with quasiperiodic potentials, though finite-size scaling of the levelspacing ratio shows a transition at $h_c^{lsr}$ which is close to thetransition point obtained from LDOS, the critical exponent obtained fromfinite-size scaling of level spacing ratio is $\nu <1$ in close similarity tothe MBL systems with random disorder.

Single-particle excitations across the localization and many-body localization transition in quasi-periodic systems