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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 states and the energy-disorder phase diagrams for up to 4 different such Lieb lattices. Via finite-size scaling, we obtain the critical properties such as critical disorders and energies as well as the universal localization lengths exponent $ u$. We find that the critical disorder $W_c$ decreases from $sim 16.5$ for the cubic lattice, to $sim 8.6$ for $mathcal{L}_3(1)$, $sim 5.9$ for $mathcal{L}_3(2)$ and $sim 4.8$ for $mathcal{L}_3(3)$. Nevertheless, the value of the critical exponent $ u$ for all Lieb lattices studied here and across disorder and energy transitions agrees within error bars with the generally accepted universal value $ u=1.590 (1.579,1.602)$.
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
We report on results of Quantum Monte Carlo simulations for bosons in a two dimensional quasi-periodic optical lattice. We study the ground state phase diagram at unity filling and confirm the existence of three phases: superfluid, Mott insulator, an
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
The gapless Bogoliubov-de Gennes (BdG) quasiparticles of a clean three dimensional spinless $p_x+ip_y$ superconductor provide an intriguing example of a thermal Hall semimetal (ThSM) phase of Majorana-Weyl fermions in class D of the Altland-Zirnbauer