Localization properties in Lieb lattices and their extensions

We study the localization properties of generalized two- and three-dimensional Lieb lattices, L2(n) L3(n), n=1,2,3 4, at energies corresponding to flat dispersive bands using transfer matrix method (TMM) finite size scaling (FSS). find that are different from in for all Ld(n). For d=3 dimensional case, states extended disorders W down W=0.01t bands, indicating disorder can lift degeneracy quickly. The phase diagram with periodic boundary condition L3(1) looks similar one hard boundaries (Liu et al., 2020). present critical Wc energy E=0 a decreasing increasing n up n=3. Last, we show table FSS parameters including so-called irrelevant variables; but results indicate accuracy is too low determine these reliably.