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We study the localization properties of generalized, two- and three-dimensional Lieb lattices, $mathcal{L}_2(n)$ and $mathcal{L}_3(n)$, $n= 1, 2, 3$ and $4$, at energies corresponding to flat and dispersive bands using the transfer matrix method (TMM) and finite size scaling (FSS). We find that the scaling properties of the flat bands are different from scaling in dispersive bands for all $mathcal{L}_d(n)$. For the $d=3$ dimensional case, states are extended for disorders $W$ down to $W=0.01 t$ at the flat bands, indicating that the disorder can lift the degeneracy of the flat bands quickly. The phase diagram with periodic boundary condition for $mathcal{L}_3(1)$ looks similar to the one for hard boundaries. We present the critical disorder $W_c$ at energy $E=0$ and find a decreasing $W_c$ for increasing $n$ for $mathcal{L}_3(n)$, up to $n=3$. Last, we show a table of FSS parameters including so-called irrelevant variables; but the results indicate that the accuracy is too low to determine these reliably. end{abstract}
We study the localization properties and the Anderson transition in the 3D Lieb lattice $mathcal{L}_3(1)$ and its extensions $mathcal{L}_3(n)$ in the presence of disorder. We compute the positions of the flat bands, the disorder-broadened density of
We study the localization properties of the two-dimensional Lieb lattice and its extensions in the presence of disorder using transfer matrix method and finite-size scaling. We find that all states in the Lieb lattice and its extensions are localized
The kicked rotor system is a textbook example of how classical and quantum dynamics can drastically differ. The energy of a classical particle confined to a ring and kicked periodically will increase linearly in time whereas in the quantum version th
Bipartite graphs are often found to represent the connectivity between the components of many systems such as ecosystems. A bipartite graph is a set of $n$ nodes that is decomposed into two disjoint subsets, having $m$ and $n-m$ vertices each, such t
We theoretically study transport properties in one-dimensional interacting quasiperiodic systems at infinite temperature. We compare and contrast the dynamical transport properties across the many-body localization (MBL) transition in quasiperiodic a