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- W4385261511 abstract "We study localization and many-body localization transition in one dimensional systems in the presence of deterministic quasi-periodic potentials. We focus on single-particle excitations obtained through single-particle Green's function in real space. A single parameter scaling analysis of the ratio of the typical to average value of the local density of states (LDOS) of single particle excitations shows that the critical exponent with which the correlation 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 the deterministic aperodic model studied here. For the interacting systems, we study single particle excitations produced in highly excited many-body eigenstates across the MBL transition and found that the critical exponent obtained from finite-size scaling of the ratio of the typical to average value of the LDOS satisfies $nu ge 1$ here as well. This analysis of local density of states shows that the localization and MBL transition in systems with quasi-periodic potentials belong to a different universality class than the localization and MBL transition in systems with random disorder where $nu ge 2$. This is in complete contrast to the level spacing ratio which is known to support the same universality class for MBL transitions in systems with quasiperiodic as well as random disorder potentials. For the interacting systems with quasiperiodic potentials, though finite-size scaling of the level spacing ratio shows a transition at $h_c^{lsr}$ which is close to the transition point obtained from LDOS, the critical exponent obtained from finite-size scaling of level spacing ratio is $nu <1$ in close similarity to the MBL systems with random disorder." @default.
- W4385261511 created "2023-07-26" @default.
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- W4385261511 date "2023-07-23" @default.
- W4385261511 modified "2023-09-23" @default.
- W4385261511 title "Single-particle excitations across the localization and many-body localization transition in quasi-periodic systems" @default.
- W4385261511 doi "https://doi.org/10.48550/arxiv.2307.12288" @default.
- W4385261511 hasPublicationYear "2023" @default.
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