Stark localization near Aubry-André criticality

• URL: http://arxiv.org/abs/2404.14971v1
• Date: Tue, 23 Apr 2024 12:25:08 GMT
• Title: Stark localization near Aubry-André criticality
• Authors: Ayan Sahoo, Aitijhya Saha, Debraj Rakshit,
• Abstract summary: We study system-dependent parameters, such as localization length, inverse participation ratio (IPR), and energy gap between the ground and first excited state, for characterizing the localization-delocalization transition. We show that the scaling exponents possessed by these key descriptors of localization are quite different from that of a pure AA model or Stark model.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work we investigate the Stark localization near the Aubry-Andr\'{e} (AA) critical point. We study system-dependent parameters, such as localization length, inverse participation ratio (IPR), and energy gap between the ground and first excited state, for characterizing the localization-delocalization transition. We show that the scaling exponents possessed by these key descriptors of localization are quite different from that of a pure AA model or Stark model. Near the critical point of the AA model, inducing Stark field of strength $h$, the localization length $\zeta$ scales as $\zeta\propto h^{-\nu}$ with $\nu\approx0.29$ which is different than both the pure AA model ($\nu=1$) and Stark model ($\nu\approx0.33$). The IPR scales as IPR $\propto h^{s}$ with $s\approx0.096$ which is again significantly different than both the pure AA model ($s\approx0.33$) and Stark model ($s\approx0.33$). The energy gap, $\Delta$, scales as $E\propto h^{\nu z}$, where $z\approx2.37$ which is however same as the pure AA model.

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